premise
stringlengths 13
2.18k
| hypothesis
stringlengths 10
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| label
stringclasses 3
values | premise_tptp
stringlengths 65
3.12k
| hypothesis_tptp
stringlengths 49
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| deberta_pred
stringclasses 3
values | proof_inputs
sequencelengths 0
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stringlengths 647
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Sharon, Charlotte are the only persons in the room.
If “everyone in the room who is not quiet or is not happy or both either is quiet or is not a happy creative person but not both” then “Sharon is the tallest in the room”.
“Sharon is the quietest in the room” if “someone in the room is not a tall wise person or is tall or both only if they is taller than Daniel”.
Sharon is tall if he/she is creative or is happy or both.
Daniel is quieter than Charlotte.
Someone in the room is a wise person if they is a happy tall creative person.
Not everyone in the room is taller than Daniel.
Sharon is the tallest in the room.
Sharon is the quietest in the room.
Only one person in the room who either is not a wise creative tall person or is not happy but not both is not creative, not tall and is not a tall creative quiet person.
At least one person in the room is not tall, not happy if they is not creative.
Everyone in the room who is a wise person or is not wise or both is creative.
Everyone in the room is not a quiet creative tall person if they is quiet.
Charlotte and Sharon are wise. | Charlotte is taller than Daniel. | contradiction | room(sharon)&room(charlotte)&(![X]:(room(X)=>(X='sharon'|X='charlotte')))&
(((![X]:(room(X)=>(((((~quiet(X))|(~happy(X))))=>(((quiet(X))<~>(~(happy(X)&creative(X)&person(X)))))))))=>(![X]:(taller(X,sharon))))&
((?[X]:(room(X)=>(((taller(daniel,X))<=(((~(tall(X)&wise(X)&person(X)))|(tall(X))))))))=>(![X]:(quieter(X,sharon))))&
(((((creative(sharon))|(happy(sharon))))=>(tall(sharon))))&
(quieter(charlotte,daniel))&
(?[X]:(room(X)=>(((happy(X)&tall(X)&creative(X)&person(X))=>(wise(X)&person(X))))))&
(~![X]:(room(X)=>(taller(daniel,X))))&
(![X]:(taller(X,sharon)))&
(![X]:(quieter(X,sharon)))&
(((?[X]:(room(X)&((((~(wise(X)&creative(X)&tall(X)&person(X)))<~>(~happy(X))))=>(((~creative(X)&~tall(X))&(~(tall(X)&creative(X)&quiet(X)&person(X))))))))&(![X,Y]:((room(X)&room(Y)&(((((~(wise(X)&creative(X)&tall(X)&person(X)))<~>(~happy(X))))=>(((~creative(X)&~tall(X))&(~(tall(X)&creative(X)&quiet(X)&person(X)))))))&(((((~(wise(Y)&creative(Y)&tall(Y)&person(Y)))<~>(~happy(Y))))=>(((~creative(Y)&~tall(Y))&(~(tall(Y)&creative(Y)&quiet(Y)&person(Y))))))))=>(X=Y)))))&
(((?[X]:(room(X)&((~creative(X))=>(~tall(X)&~happy(X)))))))&
(![X]:(room(X)=>(((((wise(X)&person(X))|(~wise(X))))=>(creative(X))))))&
(![X]:(room(X)=>(((quiet(X))=>(~(quiet(X)&creative(X)&tall(X)&person(X)))))))&
(wise(charlotte)&wise(sharon))) | room(sharon)&room(charlotte)&(![X]:(room(X)=>(X='sharon'|X='charlotte')))&
(taller(daniel,charlotte)) | contradiction | [
"hypothesis",
"p6",
"p0",
"b18",
"p7"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(taller_type, type, (
taller: ( $i * $i ) > $o)).
tff(mary_type, type, (
mary: $i)).
tff(fred_type, type, (
fred: $i)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(paul_type, type, (
paul: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(alice_type, type, (
alice: $i)).
tff(john_type, type, (
john: $i)).
tff(susan_type, type, (
susan: $i)).
tff(lucy_type, type, (
lucy: $i)).
tff(1,assumption,(X!2 = |'paul'|), introduced(assumption)).
tff(2,plain,
(|'paul'| = X!2),
inference(symmetry,[status(thm)],[1])).
tff(3,assumption,(paul = |'paul'|), introduced(assumption)).
tff(4,plain,
(|'paul'| = paul),
inference(symmetry,[status(thm)],[3])).
tff(5,plain,
(X!2 = paul),
inference(transitivity,[status(thm)],[1, 4])).
tff(6,plain,
(taller(fred, X!2) <=> taller(fred, paul)),
inference(monotonicity,[status(thm)],[5])).
tff(7,plain,
(taller(fred, paul) <=> taller(fred, X!2)),
inference(symmetry,[status(thm)],[6])).
tff(8,plain,
(taller(fred, paul) <=> taller(fred, paul)),
inference(rewrite,[status(thm)],[])).
tff(9,axiom,(((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & taller(fred, paul)), file('/mnt/tmpfs//7919132137190470380357245.p','hypothesis')).
tff(10,plain,
(taller(fred, paul)),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
(taller(fred, paul)),
inference(modus_ponens,[status(thm)],[10, 8])).
tff(12,plain,
(taller(fred, X!2)),
inference(modus_ponens,[status(thm)],[11, 7])).
tff(13,plain,
((~![X: $i] : ((~room(X)) | taller(fred, X))) <=> (~![X: $i] : ((~room(X)) | taller(fred, X)))),
inference(rewrite,[status(thm)],[])).
tff(14,plain,
((~![X: $i] : (room(X) => taller(fred, X))) <=> (~![X: $i] : ((~room(X)) | taller(fred, X)))),
inference(rewrite,[status(thm)],[])).
tff(15,axiom,(~![X: $i] : (room(X) => taller(fred, X))), file('/mnt/tmpfs//7919132137190470380357245.p','p6')).
tff(16,plain,
(~![X: $i] : ((~room(X)) | taller(fred, X))),
inference(modus_ponens,[status(thm)],[15, 14])).
tff(17,plain,
(~![X: $i] : ((~room(X)) | taller(fred, X))),
inference(modus_ponens,[status(thm)],[16, 13])).
tff(18,plain,
(~![X: $i] : ((~room(X)) | taller(fred, X))),
inference(modus_ponens,[status(thm)],[17, 13])).
tff(19,plain,
(~![X: $i] : ((~room(X)) | taller(fred, X))),
inference(modus_ponens,[status(thm)],[18, 13])).
tff(20,plain,(
~((~room(X!2)) | taller(fred, X!2))),
inference(skolemize,[status(sab)],[19])).
tff(21,plain,
(~taller(fred, X!2)),
inference(or_elim,[status(thm)],[20])).
tff(22,plain,
($false),
inference(unit_resolution,[status(thm)],[21, 12])).
tff(23,plain,((~(X!2 = |'paul'|)) | (~(paul = |'paul'|))), inference(lemma,lemma(discharge,[]))).
tff(24,plain,
(~(paul = |'paul'|)),
inference(unit_resolution,[status(thm)],[23, 1])).
tff(25,plain,
(^[X: $i] : refl(((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(26,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[25])).
tff(27,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(28,plain,
(^[X: $i] : rewrite((room(X) => ((X = |'mary'|) | (X = |'paul'|))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(29,plain,
(![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[28])).
tff(30,axiom,((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))), file('/mnt/tmpfs//7919132137190470380357245.p','p0')).
tff(31,plain,
(![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))),
inference(and_elim,[status(thm)],[30])).
tff(32,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[31, 29])).
tff(33,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[32, 27])).
tff(34,plain,(
![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[33])).
tff(35,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[34, 26])).
tff(36,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
(room(mary) & room(paul)),
inference(and_elim,[status(thm)],[30])).
tff(38,plain,
(room(paul)),
inference(and_elim,[status(thm)],[37])).
tff(39,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[38, 36])).
tff(40,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
(((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul))) <=> ((~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|)))),
inference(monotonicity,[status(thm)],[41])).
tff(43,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(transitivity,[status(thm)],[42, 40])).
tff(44,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))),
inference(quant_inst,[status(thm)],[])).
tff(45,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|)),
inference(modus_ponens,[status(thm)],[44, 43])).
tff(46,plain,
((paul = |'paul'|) | (paul = |'mary'|)),
inference(unit_resolution,[status(thm)],[45, 39, 35])).
tff(47,plain,
(paul = |'mary'|),
inference(unit_resolution,[status(thm)],[46, 24])).
tff(48,plain,
((mary = paul) <=> (mary = |'mary'|)),
inference(monotonicity,[status(thm)],[47])).
tff(49,plain,
((~(mary = paul)) <=> (~(mary = |'mary'|))),
inference(monotonicity,[status(thm)],[48])).
tff(50,plain,
((~(mary = paul)) <=> (~(mary = paul))),
inference(rewrite,[status(thm)],[])).
tff(51,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//7919132137190470380357245.p','b18')).
tff(52,plain,
(((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))),
inference(and_elim,[status(thm)],[51])).
tff(53,plain,
((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))),
inference(and_elim,[status(thm)],[52])).
tff(54,plain,
(((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))),
inference(and_elim,[status(thm)],[53])).
tff(55,plain,
((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))),
inference(and_elim,[status(thm)],[54])).
tff(56,plain,
(((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))),
inference(and_elim,[status(thm)],[55])).
tff(57,plain,
((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))),
inference(and_elim,[status(thm)],[56])).
tff(58,plain,
(((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))),
inference(and_elim,[status(thm)],[57])).
tff(59,plain,
((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))),
inference(and_elim,[status(thm)],[58])).
tff(60,plain,
(((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))),
inference(and_elim,[status(thm)],[59])).
tff(61,plain,
((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))),
inference(and_elim,[status(thm)],[60])).
tff(62,plain,
(((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))),
inference(and_elim,[status(thm)],[61])).
tff(63,plain,
((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))),
inference(and_elim,[status(thm)],[62])).
tff(64,plain,
(((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))),
inference(and_elim,[status(thm)],[63])).
tff(65,plain,
((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))),
inference(and_elim,[status(thm)],[64])).
tff(66,plain,
(((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))),
inference(and_elim,[status(thm)],[65])).
tff(67,plain,
((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))),
inference(and_elim,[status(thm)],[66])).
tff(68,plain,
(((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))),
inference(and_elim,[status(thm)],[67])).
tff(69,plain,
((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))),
inference(and_elim,[status(thm)],[68])).
tff(70,plain,
(((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))),
inference(and_elim,[status(thm)],[69])).
tff(71,plain,
((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))),
inference(and_elim,[status(thm)],[70])).
tff(72,plain,
(((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))),
inference(and_elim,[status(thm)],[71])).
tff(73,plain,
((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))),
inference(and_elim,[status(thm)],[72])).
tff(74,plain,
(((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))),
inference(and_elim,[status(thm)],[73])).
tff(75,plain,
((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))),
inference(and_elim,[status(thm)],[74])).
tff(76,plain,
(((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))),
inference(and_elim,[status(thm)],[75])).
tff(77,plain,
((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))),
inference(and_elim,[status(thm)],[76])).
tff(78,plain,
(((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))),
inference(and_elim,[status(thm)],[77])).
tff(79,plain,
((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))),
inference(and_elim,[status(thm)],[78])).
tff(80,plain,
(((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))),
inference(and_elim,[status(thm)],[79])).
tff(81,plain,
((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))),
inference(and_elim,[status(thm)],[80])).
tff(82,plain,
(((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))),
inference(and_elim,[status(thm)],[81])).
tff(83,plain,
((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))),
inference(and_elim,[status(thm)],[82])).
tff(84,plain,
(((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))),
inference(and_elim,[status(thm)],[83])).
tff(85,plain,
((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))),
inference(and_elim,[status(thm)],[84])).
tff(86,plain,
(((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))),
inference(and_elim,[status(thm)],[85])).
tff(87,plain,
((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))),
inference(and_elim,[status(thm)],[86])).
tff(88,plain,
(((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))),
inference(and_elim,[status(thm)],[87])).
tff(89,plain,
((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))),
inference(and_elim,[status(thm)],[88])).
tff(90,plain,
(((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))),
inference(and_elim,[status(thm)],[89])).
tff(91,plain,
((~(mary = paul)) & (~(mary = fred))),
inference(and_elim,[status(thm)],[90])).
tff(92,plain,
(~(mary = paul)),
inference(and_elim,[status(thm)],[91])).
tff(93,plain,
(~(mary = paul)),
inference(modus_ponens,[status(thm)],[92, 50])).
tff(94,plain,
(~(mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[93, 49])).
tff(95,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(96,plain,
(room(mary)),
inference(and_elim,[status(thm)],[37])).
tff(97,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[96, 95])).
tff(98,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(99,plain,
(((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary))) <=> ((~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(100,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|)))),
inference(monotonicity,[status(thm)],[99])).
tff(101,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(transitivity,[status(thm)],[100, 98])).
tff(102,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))),
inference(quant_inst,[status(thm)],[])).
tff(103,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[102, 101])).
tff(104,plain,
((mary = |'paul'|) | (mary = |'mary'|)),
inference(unit_resolution,[status(thm)],[103, 97, 35])).
tff(105,plain,
(mary = |'paul'|),
inference(unit_resolution,[status(thm)],[104, 94])).
tff(106,plain,
(mary = X!2),
inference(transitivity,[status(thm)],[105, 2])).
tff(107,plain,
(taller(fred, mary) <=> taller(fred, X!2)),
inference(monotonicity,[status(thm)],[106])).
tff(108,plain,
(taller(fred, X!2) <=> taller(fred, mary)),
inference(symmetry,[status(thm)],[107])).
tff(109,plain,
((~taller(fred, X!2)) <=> (~taller(fred, mary))),
inference(monotonicity,[status(thm)],[108])).
tff(110,plain,
(~taller(fred, mary)),
inference(modus_ponens,[status(thm)],[21, 109])).
tff(111,plain,
(^[X: $i] : refl(taller(X, mary) <=> taller(X, mary))),
inference(bind,[status(th)],[])).
tff(112,plain,
(![X: $i] : taller(X, mary) <=> ![X: $i] : taller(X, mary)),
inference(quant_intro,[status(thm)],[111])).
tff(113,plain,
(![X: $i] : taller(X, mary) <=> ![X: $i] : taller(X, mary)),
inference(rewrite,[status(thm)],[])).
tff(114,axiom,(![X: $i] : taller(X, mary)), file('/mnt/tmpfs//7919132137190470380357245.p','p7')).
tff(115,plain,
(![X: $i] : taller(X, mary)),
inference(modus_ponens,[status(thm)],[114, 113])).
tff(116,plain,(
![X: $i] : taller(X, mary)),
inference(skolemize,[status(sab)],[115])).
tff(117,plain,
(![X: $i] : taller(X, mary)),
inference(modus_ponens,[status(thm)],[116, 112])).
tff(118,plain,
((~![X: $i] : taller(X, mary)) | taller(fred, mary)),
inference(quant_inst,[status(thm)],[])).
tff(119,plain,
(taller(fred, mary)),
inference(unit_resolution,[status(thm)],[118, 117])).
tff(120,plain,
($false),
inference(unit_resolution,[status(thm)],[119, 110])).
tff(121,plain,(~(X!2 = |'paul'|)), inference(lemma,lemma(discharge,[]))).
tff(122,plain,
(room(X!2)),
inference(or_elim,[status(thm)],[20])).
tff(123,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(X!2)) | (X!2 = |'paul'|) | (X!2 = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(X!2)) | (X!2 = |'paul'|) | (X!2 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(124,plain,
(((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))) <=> ((~room(X!2)) | (X!2 = |'paul'|) | (X!2 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(125,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(X!2)) | (X!2 = |'paul'|) | (X!2 = |'mary'|)))),
inference(monotonicity,[status(thm)],[124])).
tff(126,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(X!2)) | (X!2 = |'paul'|) | (X!2 = |'mary'|))),
inference(transitivity,[status(thm)],[125, 123])).
tff(127,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))),
inference(quant_inst,[status(thm)],[])).
tff(128,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(X!2)) | (X!2 = |'paul'|) | (X!2 = |'mary'|)),
inference(modus_ponens,[status(thm)],[127, 126])).
tff(129,plain,
((X!2 = |'paul'|) | (X!2 = |'mary'|)),
inference(unit_resolution,[status(thm)],[128, 35, 122])).
tff(130,plain,
(X!2 = |'mary'|),
inference(unit_resolution,[status(thm)],[129, 121])).
tff(131,plain,
(|'mary'| = X!2),
inference(symmetry,[status(thm)],[130])).
tff(132,assumption,(paul = |'mary'|), introduced(assumption)).
tff(133,plain,
(|'mary'| = paul),
inference(symmetry,[status(thm)],[132])).
tff(134,assumption,(X!2 = |'mary'|), introduced(assumption)).
tff(135,plain,
(X!2 = paul),
inference(transitivity,[status(thm)],[134, 133])).
tff(136,plain,
(taller(fred, X!2) <=> taller(fred, paul)),
inference(monotonicity,[status(thm)],[135])).
tff(137,plain,
(taller(fred, paul) <=> taller(fred, X!2)),
inference(symmetry,[status(thm)],[136])).
tff(138,plain,
(taller(fred, X!2)),
inference(modus_ponens,[status(thm)],[11, 137])).
tff(139,plain,
($false),
inference(unit_resolution,[status(thm)],[21, 138])).
tff(140,plain,((~(X!2 = |'mary'|)) | (~(paul = |'mary'|))), inference(lemma,lemma(discharge,[]))).
tff(141,plain,
(~(paul = |'mary'|)),
inference(unit_resolution,[status(thm)],[140, 130])).
tff(142,plain,
(paul = |'paul'|),
inference(unit_resolution,[status(thm)],[46, 141])).
tff(143,plain,
((mary = paul) <=> (mary = |'paul'|)),
inference(monotonicity,[status(thm)],[142])).
tff(144,plain,
((~(mary = paul)) <=> (~(mary = |'paul'|))),
inference(monotonicity,[status(thm)],[143])).
tff(145,plain,
(~(mary = |'paul'|)),
inference(modus_ponens,[status(thm)],[93, 144])).
tff(146,plain,
(mary = |'mary'|),
inference(unit_resolution,[status(thm)],[104, 145])).
tff(147,plain,
(mary = X!2),
inference(transitivity,[status(thm)],[146, 131])).
tff(148,plain,
(taller(fred, mary) <=> taller(fred, X!2)),
inference(monotonicity,[status(thm)],[147])).
tff(149,plain,
(taller(fred, X!2) <=> taller(fred, mary)),
inference(symmetry,[status(thm)],[148])).
tff(150,plain,
((~taller(fred, X!2)) <=> (~taller(fred, mary))),
inference(monotonicity,[status(thm)],[149])).
tff(151,plain,
(~taller(fred, mary)),
inference(modus_ponens,[status(thm)],[21, 150])).
tff(152,plain,
($false),
inference(unit_resolution,[status(thm)],[119, 151])).
% SZS output end Proof
|
Carl, Trevor, Fred, Maria, Maria are the only persons in the room.
Either "everyone in the room does not have lived in exactly three countries or has completed a triathlon or both" or "someone in the room has a pet dog" or but not both.
"Carl has lived in exactly three countries or does not have lived in exactly three countries or both" only if "at least one person in the room has completed a triathlon".
At least one person in the room has completed a triathlon.
More than one person in the room who is not a client of Meta has lived in exactly three countries.
Everyone in the room is a client of Meta or does not have completed a triathlon or both.
Everyone in the room does not have lived in exactly three countries or does not have completed a triathlon or both.
Carl has a pet dog.
More than one person in the room does not have a pet dog if they has completed a triathlon and is not a client of Meta. | Everyone outside the room does not have a pet dog and has a pet dog if they has completed a triathlon. | neutral | room(carl)&room(trevor)&room(fred)&room(maria)&room(maria)&(![X]:(room(X)=>(X='carl'|X='trevor'|X='fred'|X='maria'|X='maria')))&
(((![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))|(has_completed_a_triathlon(X))))))<~>(?[X]:(room(X)=>(has_a_pet_dog(X)))))&
((((has_lived_in_exactly_three_countries(carl))|(does_not_have_lived_in_exactly_three_countries(carl))))=>(((?[X]:(room(X)&has_completed_a_triathlon(X))))))&
(((?[X]:(room(X)&has_completed_a_triathlon(X)))))&
((?[X,Y]:(room(X)&room(Y)&(((is_not_a_client_of_Meta(X))=>(has_lived_in_exactly_three_countries(X)))&((is_not_a_client_of_Meta(Y))=>(has_lived_in_exactly_three_countries(Y))))&(X!=Y))))&
(![X]:(room(X)=>(((is_a_client_of_Meta(X))|(does_not_have_completed_a_triathlon(X))))))&
(![X]:(room(X)=>(((does_not_have_lived_in_exactly_three_countries(X))|(does_not_have_completed_a_triathlon(X))))))&
(has_a_pet_dog(carl))&
((?[X,Y]:(room(X)&room(Y)&(((((has_completed_a_triathlon(X))&(is_not_a_client_of_Meta(X))))=>(does_not_have_a_pet_dog(X)))&((((has_completed_a_triathlon(Y))&(is_not_a_client_of_Meta(Y))))=>(does_not_have_a_pet_dog(Y))))&(X!=Y))))) | room(carl)&room(trevor)&room(fred)&room(maria)&room(maria)&(![X]:(room(X)=>(X='carl'|X='trevor'|X='fred'|X='maria'|X='maria')))&
(![X]:(~room(X)=>(((has_completed_a_triathlon(X))=>(((does_not_have_a_pet_dog(X))&(has_a_pet_dog(X)))))))) | contradiction | [] | null |
Genoveva, Otto, Larry, Richard are the only persons in the room. If “Larry is the quietest in the room” then “everyone in the room is not a happy creative person”. If “not everyone in the room who is not a tall person is not a wise person or is not a rich person or both” then “Otto is not a old person and is not quiet, not old, not rich”. It is not the case that “it is not the case that “Genoveva is happy if he/she is wise””. Not everyone in the room who is not a tall person is not a wise person or is not a rich person or both. It is not the case that “Marie is older than Genoveva”. Someone in the room is not a rich person. Richard is not a rich person. Otto is not a rich person. Genoveva is not a rich person. | It is not the case that “Otto is not rich”. | contradiction | room(genoveva)&room(otto)&room(larry)&room(richard)&(![X]:(room(X)=>(X='genoveva'|X='otto'|X='larry'|X='richard')))&
(((![X]:(quieter(X,larry)))=>(![X]:(room(X)=>(~(happy(X)&creative(X)&person(X))))))&
((~![X]:(room(X)=>(((~(tall(X)&person(X)))=>(((~(wise(X)&person(X)))|(~(rich(X)&person(X)))))))))=>(((~(old(otto)&person(otto)))&(~quiet(otto)&~old(otto)&~rich(otto)))))&
(~(~(((wise(genoveva))=>(happy(genoveva))))))&
(~![X]:(room(X)=>(((~(tall(X)&person(X)))=>(((~(wise(X)&person(X)))|(~(rich(X)&person(X)))))))))&
(~(older(genoveva,marie)))&
(?[X]:(room(X)=>(~(rich(X)&person(X)))))&
(~(rich(richard)&person(richard)))&
(~(rich(otto)&person(otto)))&
(~(rich(genoveva)&person(genoveva)))) | room(genoveva)&room(otto)&room(larry)&room(richard)&(![X]:(room(X)=>(X='genoveva'|X='otto'|X='larry'|X='richard')))&
(~(~rich(otto))) | contradiction | [
"p4",
"hypothesis",
"p2"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(tall_type, type, (
tall: $i > $o)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(room_type, type, (
room: $i > $o)).
tff(wise_type, type, (
wise: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(old_type, type, (
old: $i > $o)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(alice_type, type, (
alice: $i)).
tff(fred_type, type, (
fred: $i)).
tff(mary_type, type, (
mary: $i)).
tff(1,plain,
((~((~(rich(X!1) & person(X!1))) | (~(wise(X!1) & person(X!1))) | (tall(X!1) & person(X!1)) | (~room(X!1)))) <=> (~((~(rich(X!1) & person(X!1))) | (~(wise(X!1) & person(X!1))) | (tall(X!1) & person(X!1)) | (~room(X!1))))),
inference(rewrite,[status(thm)],[])).
tff(2,plain,
((~![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))) <=> (~![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(3,plain,
((~![X: $i] : (room(X) => ((~(tall(X) & person(X))) => ((~(wise(X) & person(X))) | (~(rich(X) & person(X))))))) <=> (~![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(4,axiom,(~![X: $i] : (room(X) => ((~(tall(X) & person(X))) => ((~(wise(X) & person(X))) | (~(rich(X) & person(X))))))), file('/mnt/tmpfs//4454898607949819011128578.p','p4')).
tff(5,plain,
(~![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))),
inference(modus_ponens,[status(thm)],[4, 3])).
tff(6,plain,
(~![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))),
inference(modus_ponens,[status(thm)],[5, 2])).
tff(7,plain,(
~((~(rich(X!1) & person(X!1))) | (~(wise(X!1) & person(X!1))) | (tall(X!1) & person(X!1)) | (~room(X!1)))),
inference(skolemize,[status(sab)],[6])).
tff(8,plain,
(~((~(rich(X!1) & person(X!1))) | (~(wise(X!1) & person(X!1))) | (tall(X!1) & person(X!1)) | (~room(X!1)))),
inference(modus_ponens,[status(thm)],[7, 1])).
tff(9,plain,
(rich(X!1) & person(X!1)),
inference(or_elim,[status(thm)],[8])).
tff(10,plain,
(person(X!1)),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
((~(~((~tall(X!1)) | (~person(X!1))))) <=> ((~tall(X!1)) | (~person(X!1)))),
inference(rewrite,[status(thm)],[])).
tff(12,plain,
((tall(X!1) & person(X!1)) <=> (~((~tall(X!1)) | (~person(X!1))))),
inference(rewrite,[status(thm)],[])).
tff(13,plain,
((~(tall(X!1) & person(X!1))) <=> (~(~((~tall(X!1)) | (~person(X!1)))))),
inference(monotonicity,[status(thm)],[12])).
tff(14,plain,
((~(tall(X!1) & person(X!1))) <=> ((~tall(X!1)) | (~person(X!1)))),
inference(transitivity,[status(thm)],[13, 11])).
tff(15,plain,
(~(tall(X!1) & person(X!1))),
inference(or_elim,[status(thm)],[8])).
tff(16,plain,
((~tall(X!1)) | (~person(X!1))),
inference(modus_ponens,[status(thm)],[15, 14])).
tff(17,plain,
(~tall(X!1)),
inference(unit_resolution,[status(thm)],[16, 10])).
tff(18,plain,
(((~person(X!1)) | (~tall(X!1))) | tall(X!1)),
inference(tautology,[status(thm)],[])).
tff(19,plain,
((~person(X!1)) | (~tall(X!1))),
inference(unit_resolution,[status(thm)],[18, 17])).
tff(20,plain,
(room(X!1)),
inference(or_elim,[status(thm)],[8])).
tff(21,plain,
(wise(X!1) & person(X!1)),
inference(or_elim,[status(thm)],[8])).
tff(22,plain,
(wise(X!1)),
inference(and_elim,[status(thm)],[21])).
tff(23,plain,
(rich(X!1)),
inference(and_elim,[status(thm)],[9])).
tff(24,plain,
(rich(paul) <=> rich(paul)),
inference(rewrite,[status(thm)],[])).
tff(25,plain,
((~(~rich(paul))) <=> rich(paul)),
inference(rewrite,[status(thm)],[])).
tff(26,axiom,(((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & (~(~rich(paul)))), file('/mnt/tmpfs//4454898607949819011128578.p','hypothesis')).
tff(27,plain,
(~(~rich(paul))),
inference(and_elim,[status(thm)],[26])).
tff(28,plain,
(rich(paul)),
inference(modus_ponens,[status(thm)],[27, 25])).
tff(29,plain,
(rich(paul)),
inference(modus_ponens,[status(thm)],[28, 24])).
tff(30,plain,
((old(paul) | quiet(paul) | rich(paul)) | (~rich(paul))),
inference(tautology,[status(thm)],[])).
tff(31,plain,
(old(paul) | quiet(paul) | rich(paul)),
inference(unit_resolution,[status(thm)],[30, 29])).
tff(32,plain,
(((~(old(paul) | quiet(paul) | rich(paul))) | ![X: $i] : ((~room(X)) | (~person(X)) | (~rich(X)) | (~wise(X)) | (~((~person(X)) | (~tall(X)))))) <=> ((~(old(paul) | quiet(paul) | rich(paul))) | ![X: $i] : ((~room(X)) | (~person(X)) | (~rich(X)) | (~wise(X)) | (~((~person(X)) | (~tall(X))))))),
inference(rewrite,[status(thm)],[])).
tff(33,plain,
((((~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))) <=> ((~(old(paul) | quiet(paul) | rich(paul))) | ![X: $i] : ((~room(X)) | (~person(X)) | (~rich(X)) | (~wise(X)) | (~((~person(X)) | (~tall(X))))))),
inference(rewrite,[status(thm)],[])).
tff(34,plain,
((((~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))) <=> (((~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(35,plain,
((((~(old(paul) & person(paul))) & (~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))) <=> (((~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
((((~(old(paul) & person(paul))) & (~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))) <=> (((~(old(paul) & person(paul))) & (~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
(((~![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))) => ((~(old(paul) & person(paul))) & (~quiet(paul)) & (~old(paul)) & (~rich(paul)))) <=> (((~(old(paul) & person(paul))) & (~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(38,plain,
(((~(old(paul) & person(paul))) & ((~quiet(paul)) & (~old(paul)) & (~rich(paul)))) <=> ((~(old(paul) & person(paul))) & (~quiet(paul)) & (~old(paul)) & (~rich(paul)))),
inference(rewrite,[status(thm)],[])).
tff(39,plain,
((((~quiet(paul)) & (~old(paul))) & (~rich(paul))) <=> ((~quiet(paul)) & (~old(paul)) & (~rich(paul)))),
inference(rewrite,[status(thm)],[])).
tff(40,plain,
(((~(old(paul) & person(paul))) & (((~quiet(paul)) & (~old(paul))) & (~rich(paul)))) <=> ((~(old(paul) & person(paul))) & ((~quiet(paul)) & (~old(paul)) & (~rich(paul))))),
inference(monotonicity,[status(thm)],[39])).
tff(41,plain,
(((~(old(paul) & person(paul))) & (((~quiet(paul)) & (~old(paul))) & (~rich(paul)))) <=> ((~(old(paul) & person(paul))) & (~quiet(paul)) & (~old(paul)) & (~rich(paul)))),
inference(transitivity,[status(thm)],[40, 38])).
tff(42,plain,
(((~![X: $i] : (room(X) => ((~(tall(X) & person(X))) => ((~(wise(X) & person(X))) | (~(rich(X) & person(X))))))) => ((~(old(paul) & person(paul))) & (((~quiet(paul)) & (~old(paul))) & (~rich(paul))))) <=> ((~![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))) => ((~(old(paul) & person(paul))) & (~quiet(paul)) & (~old(paul)) & (~rich(paul))))),
inference(monotonicity,[status(thm)],[3, 41])).
tff(43,plain,
(((~![X: $i] : (room(X) => ((~(tall(X) & person(X))) => ((~(wise(X) & person(X))) | (~(rich(X) & person(X))))))) => ((~(old(paul) & person(paul))) & (((~quiet(paul)) & (~old(paul))) & (~rich(paul))))) <=> (((~(old(paul) & person(paul))) & (~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X))))),
inference(transitivity,[status(thm)],[42, 37])).
tff(44,axiom,((~![X: $i] : (room(X) => ((~(tall(X) & person(X))) => ((~(wise(X) & person(X))) | (~(rich(X) & person(X))))))) => ((~(old(paul) & person(paul))) & (((~quiet(paul)) & (~old(paul))) & (~rich(paul))))), file('/mnt/tmpfs//4454898607949819011128578.p','p2')).
tff(45,plain,
(((~(old(paul) & person(paul))) & (~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))),
inference(modus_ponens,[status(thm)],[44, 43])).
tff(46,plain,
(((~(old(paul) & person(paul))) & (~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))),
inference(modus_ponens,[status(thm)],[45, 36])).
tff(47,plain,
(((~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))),
inference(modus_ponens,[status(thm)],[46, 35])).
tff(48,plain,
(((~quiet(paul)) & (~old(paul)) & (~rich(paul))) | ![X: $i] : ((~(rich(X) & person(X))) | (~(wise(X) & person(X))) | (tall(X) & person(X)) | (~room(X)))),
inference(modus_ponens,[status(thm)],[47, 34])).
|
Christopher, Krista, Donald are the only persons in the room.
If “only one person in the room does not enjoy kayaking” then “Christopher ~predf”.
It is not the case that “Christopher does not enjoy logic puzzles if he/she predf, bakes bread at home and reads mystery novels”.
Everyone in the room either enjoys kayaking or predf but not both.
Everyone in the room reads mystery novels.
Christopher enjoys logic puzzles if he/she enjoys kayaking and does not enjoy kayaking. | Christopher enjoys kayaking. | contradiction | room(christopher)&room(krista)&room(donald)&(![X]:(room(X)=>(X='christopher'|X='krista'|X='donald')))&
(((((?[X]:(room(X)&does_not_enjoy_kayaking(X)))&(![X,Y]:((room(X)&room(Y)&(does_not_enjoy_kayaking(X))&(does_not_enjoy_kayaking(Y)))=>(X=Y)))))=>(~predf(christopher)))&
(~(((((predf(christopher))&(bakes_bread_at_home(christopher))&(reads_mystery_novels(christopher))))=>(does_not_enjoy_logic_puzzles(christopher)))))&
(![X]:(room(X)=>(((enjoys_kayaking(X))<~>(predf(X))))))&
(![X]:(room(X)=>(reads_mystery_novels(X))))&
(((((enjoys_kayaking(christopher))&(does_not_enjoy_kayaking(christopher))))=>(enjoys_logic_puzzles(christopher))))) | room(christopher)&room(krista)&room(donald)&(![X]:(room(X)=>(X='christopher'|X='krista'|X='donald')))&
(enjoys_kayaking(christopher)) | entailment | [
"hypothesis",
"p2",
"p3",
"p0"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(predf_type, type, (
predf: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(predd_type, type, (
predd: $i > $o)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(fred_type, type, (
fred: $i)).
tff(paul_type, type, (
paul: $i)).
tff(prede_type, type, (
prede: $i > $o)).
tff(predb_type, type, (
predb: $i > $o)).
tff(preda_type, type, (
preda: $i > $o)).
tff(1,plain,
(predd(mary) <=> predd(mary)),
inference(rewrite,[status(thm)],[])).
tff(2,axiom,((((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))) & predd(mary)), file('/mnt/tmpfs//8774497907839960313648609.p','hypothesis')).
tff(3,plain,
(predd(mary)),
inference(and_elim,[status(thm)],[2])).
tff(4,plain,
(predd(mary)),
inference(modus_ponens,[status(thm)],[3, 1])).
tff(5,plain,
(predf(mary) <=> predf(mary)),
inference(rewrite,[status(thm)],[])).
tff(6,plain,
((~(((predf(mary) & predb(mary)) & prede(mary)) => (~preda(mary)))) <=> (~((~preda(mary)) | (~(predf(mary) & predb(mary) & prede(mary)))))),
inference(rewrite,[status(thm)],[])).
tff(7,axiom,(~(((predf(mary) & predb(mary)) & prede(mary)) => (~preda(mary)))), file('/mnt/tmpfs//8774497907839960313648609.p','p2')).
tff(8,plain,
(~((~preda(mary)) | (~(predf(mary) & predb(mary) & prede(mary))))),
inference(modus_ponens,[status(thm)],[7, 6])).
tff(9,plain,
(predf(mary) & predb(mary) & prede(mary)),
inference(or_elim,[status(thm)],[8])).
tff(10,plain,
(predf(mary)),
inference(and_elim,[status(thm)],[9])).
tff(11,plain,
(predf(mary)),
inference(modus_ponens,[status(thm)],[10, 5])).
tff(12,plain,
((predd(mary) <=> predf(mary)) | (~predd(mary)) | (~predf(mary))),
inference(tautology,[status(thm)],[])).
tff(13,plain,
(predd(mary) <=> predf(mary)),
inference(unit_resolution,[status(thm)],[12, 11, 4])).
tff(14,plain,
(^[X: $i] : refl(((~room(X)) | (~(predd(X) <=> predf(X)))) <=> ((~room(X)) | (~(predd(X) <=> predf(X)))))),
inference(bind,[status(th)],[])).
tff(15,plain,
(![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X)))) <=> ![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X))))),
inference(quant_intro,[status(thm)],[14])).
tff(16,plain,
(![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X)))) <=> ![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X))))),
inference(rewrite,[status(thm)],[])).
tff(17,plain,
(^[X: $i] : trans(monotonicity(rewrite((~(predd(X) <=> predf(X))) <=> (~(predd(X) <=> predf(X)))), ((room(X) => (~(predd(X) <=> predf(X)))) <=> (room(X) => (~(predd(X) <=> predf(X)))))), rewrite((room(X) => (~(predd(X) <=> predf(X)))) <=> ((~room(X)) | (~(predd(X) <=> predf(X))))), ((room(X) => (~(predd(X) <=> predf(X)))) <=> ((~room(X)) | (~(predd(X) <=> predf(X))))))),
inference(bind,[status(th)],[])).
tff(18,plain,
(![X: $i] : (room(X) => (~(predd(X) <=> predf(X)))) <=> ![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X))))),
inference(quant_intro,[status(thm)],[17])).
tff(19,axiom,(![X: $i] : (room(X) => (~(predd(X) <=> predf(X))))), file('/mnt/tmpfs//8774497907839960313648609.p','p3')).
tff(20,plain,
(![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X))))),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,
(![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X))))),
inference(modus_ponens,[status(thm)],[20, 16])).
tff(22,plain,(
![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X))))),
inference(skolemize,[status(sab)],[21])).
tff(23,plain,
(![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X))))),
inference(modus_ponens,[status(thm)],[22, 15])).
tff(24,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(25,axiom,(((room(mary) & room(paul)) & room(fred)) & ![X: $i] : (room(X) => (((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)))), file('/mnt/tmpfs//8774497907839960313648609.p','p0')).
tff(26,plain,
((room(mary) & room(paul)) & room(fred)),
inference(and_elim,[status(thm)],[25])).
tff(27,plain,
(room(mary) & room(paul)),
inference(and_elim,[status(thm)],[26])).
tff(28,plain,
(room(mary)),
inference(and_elim,[status(thm)],[27])).
tff(29,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[28, 24])).
tff(30,plain,
(((~![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X))))) | ((~room(mary)) | (~(predd(mary) <=> predf(mary))))) <=> ((~![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X))))) | (~room(mary)) | (~(predd(mary) <=> predf(mary))))),
inference(rewrite,[status(thm)],[])).
tff(31,plain,
((~![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X))))) | ((~room(mary)) | (~(predd(mary) <=> predf(mary))))),
inference(quant_inst,[status(thm)],[])).
tff(32,plain,
((~![X: $i] : ((~room(X)) | (~(predd(X) <=> predf(X))))) | (~room(mary)) | (~(predd(mary) <=> predf(mary)))),
inference(modus_ponens,[status(thm)],[31, 30])).
tff(33,plain,
($false),
inference(unit_resolution,[status(thm)],[32, 29, 23, 13])).
% SZS output end Proof
|
Elenora, Tonya, Elizabeth are the only persons in the room.
If “everyone in the room is older than Catherine if they is not hated by Hattie and is not old” then “no one in the room owns a microscope and does not hate Catherine”.
“Everyone in the room is a brave wise european and is a brave european” unless “not everyone anywhere is not a brave old european if they is not a old wise european and uses contact lenses”.
Someone in the room who is brave either is not old or does not use contact lenses but not both.
Everyone in the room does not use contact lenses.
Not everyone in the room is not a brave old wise european and enjoys stand-up paddleboarding.
Everyone outside the room is not a old person, ~predf and is not brave.
Elenora who does not hate Hattie is older than Catherine.
Elenora owns a microscope and enjoys stand-up paddleboarding. | Tonya is wise. | entailment | room(elenora)&room(tonya)&room(elizabeth)&(![X]:(room(X)=>(X='elenora'|X='tonya'|X='elizabeth')))&
(((![X]:(room(X)=>(((((~hate(X,hattie))&(~old(X))))=>(older(catherine,X))))))=>(~?[X]:(room(X)=>(((owns_a_microscope(X))&(~hate(catherine,X)))))))&
(~(~![X]:(anywhere(X)=>(((((~(old(X)&wise(X)&european(X)))&(uses_contact_lenses(X))))=>(~(brave(X)&old(X)&european(X)))))))=>(![X]:(room(X)=>(((brave(X)&wise(X)&european(X))&(brave(X)&european(X)))))))&
(?[X]:(room(X)=>(((brave(X))=>(((~old(X))<~>(does_not_use_contact_lenses(X))))))))&
(![X]:(room(X)=>(does_not_use_contact_lenses(X))))&
(~![X]:(room(X)=>(((~(brave(X)&old(X)&wise(X)&european(X)))&(enjoys_stand-up_paddleboarding(X))))))&
(![X]:(~room(X)=>(((~(old(X)&person(X)))&(~predf(X))&(~brave(X))))))&
((~hate(hattie,elenora))&(older(catherine,elenora)))&
(((owns_a_microscope(elenora))&(enjoys_stand-up_paddleboarding(elenora))))) | room(elenora)&room(tonya)&room(elizabeth)&(![X]:(room(X)=>(X='elenora'|X='tonya'|X='elizabeth')))&
(wise(tonya)) | neutral | [
"p4",
"p6",
"p2"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(wise_type, type, (
wise: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(european_type, type, (
european: $i > $o)).
tff(brave_type, type, (
brave: $i > $o)).
tff(predc_type, type, (
predc: $i > $o)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(old_type, type, (
old: $i > $o)).
tff(anywhere_type, type, (
anywhere: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(predf_type, type, (
predf: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(fred_type, type, (
fred: $i)).
tff(1,assumption,(~((~anywhere(X!1)) | (~brave(X!1)) | (~old(X!1)) | (~european(X!1)) | (~((~old(X!1)) | (~european(X!1)) | (~wise(X!1)))) | (~predc(X!1)))), introduced(assumption)).
tff(2,plain,
(((~anywhere(X!1)) | (~brave(X!1)) | (~old(X!1)) | (~european(X!1)) | (~((~old(X!1)) | (~european(X!1)) | (~wise(X!1)))) | (~predc(X!1))) | brave(X!1)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(brave(X!1)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
((brave(X!1) | predf(X!1) | (~((~old(X!1)) | (~person(X!1))))) | (~brave(X!1))),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(brave(X!1) | predf(X!1) | (~((~old(X!1)) | (~person(X!1))))),
inference(unit_resolution,[status(thm)],[4, 3])).
tff(6,plain,
(^[X: $i] : refl(((~predc(X)) | (~room(X))) <=> ((~predc(X)) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(7,plain,
(![X: $i] : ((~predc(X)) | (~room(X))) <=> ![X: $i] : ((~predc(X)) | (~room(X)))),
inference(quant_intro,[status(thm)],[6])).
tff(8,plain,
(![X: $i] : ((~predc(X)) | (~room(X))) <=> ![X: $i] : ((~predc(X)) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(9,plain,
(^[X: $i] : rewrite((room(X) => (~predc(X))) <=> ((~predc(X)) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(10,plain,
(![X: $i] : (room(X) => (~predc(X))) <=> ![X: $i] : ((~predc(X)) | (~room(X)))),
inference(quant_intro,[status(thm)],[9])).
tff(11,axiom,(![X: $i] : (room(X) => (~predc(X)))), file('/mnt/tmpfs//1375177612931774584832018.p','p4')).
tff(12,plain,
(![X: $i] : ((~predc(X)) | (~room(X)))),
inference(modus_ponens,[status(thm)],[11, 10])).
tff(13,plain,
(![X: $i] : ((~predc(X)) | (~room(X)))),
inference(modus_ponens,[status(thm)],[12, 8])).
tff(14,plain,(
![X: $i] : ((~predc(X)) | (~room(X)))),
inference(skolemize,[status(sab)],[13])).
tff(15,plain,
(![X: $i] : ((~predc(X)) | (~room(X)))),
inference(modus_ponens,[status(thm)],[14, 7])).
tff(16,plain,
(((~anywhere(X!1)) | (~brave(X!1)) | (~old(X!1)) | (~european(X!1)) | (~((~old(X!1)) | (~european(X!1)) | (~wise(X!1)))) | (~predc(X!1))) | predc(X!1)),
inference(tautology,[status(thm)],[])).
tff(17,plain,
(predc(X!1)),
inference(unit_resolution,[status(thm)],[16, 1])).
tff(18,plain,
(((~![X: $i] : ((~predc(X)) | (~room(X)))) | ((~predc(X!1)) | (~room(X!1)))) <=> ((~![X: $i] : ((~predc(X)) | (~room(X)))) | (~predc(X!1)) | (~room(X!1)))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~![X: $i] : ((~predc(X)) | (~room(X)))) | ((~predc(X!1)) | (~room(X!1)))),
inference(quant_inst,[status(thm)],[])).
tff(20,plain,
((~![X: $i] : ((~predc(X)) | (~room(X)))) | (~predc(X!1)) | (~room(X!1))),
inference(modus_ponens,[status(thm)],[19, 18])).
tff(21,plain,
(~room(X!1)),
inference(unit_resolution,[status(thm)],[20, 17, 15])).
tff(22,plain,
(^[X: $i] : refl((room(X) | (~(brave(X) | predf(X) | (~((~old(X)) | (~person(X))))))) <=> (room(X) | (~(brave(X) | predf(X) | (~((~old(X)) | (~person(X))))))))),
inference(bind,[status(th)],[])).
tff(23,plain,
(![X: $i] : (room(X) | (~(brave(X) | predf(X) | (~((~old(X)) | (~person(X))))))) <=> ![X: $i] : (room(X) | (~(brave(X) | predf(X) | (~((~old(X)) | (~person(X)))))))),
inference(quant_intro,[status(thm)],[22])).
tff(24,plain,
(^[X: $i] : rewrite((room(X) | ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X)))) <=> (room(X) | (~(brave(X) | predf(X) | (~((~old(X)) | (~person(X))))))))),
inference(bind,[status(th)],[])).
tff(25,plain,
(![X: $i] : (room(X) | ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X)))) <=> ![X: $i] : (room(X) | (~(brave(X) | predf(X) | (~((~old(X)) | (~person(X)))))))),
inference(quant_intro,[status(thm)],[24])).
tff(26,plain,
(![X: $i] : (room(X) | ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X)))) <=> ![X: $i] : (room(X) | ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X))))),
inference(rewrite,[status(thm)],[])).
tff(27,plain,
(^[X: $i] : trans(monotonicity(rewrite((((~(old(X) & person(X))) & (~predf(X))) & (~brave(X))) <=> ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X)))), (((~room(X)) => (((~(old(X) & person(X))) & (~predf(X))) & (~brave(X)))) <=> ((~room(X)) => ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X)))))), rewrite(((~room(X)) => ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X)))) <=> (room(X) | ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X))))), (((~room(X)) => (((~(old(X) & person(X))) & (~predf(X))) & (~brave(X)))) <=> (room(X) | ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X))))))),
inference(bind,[status(th)],[])).
tff(28,plain,
(![X: $i] : ((~room(X)) => (((~(old(X) & person(X))) & (~predf(X))) & (~brave(X)))) <=> ![X: $i] : (room(X) | ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X))))),
inference(quant_intro,[status(thm)],[27])).
tff(29,axiom,(![X: $i] : ((~room(X)) => (((~(old(X) & person(X))) & (~predf(X))) & (~brave(X))))), file('/mnt/tmpfs//1375177612931774584832018.p','p6')).
tff(30,plain,
(![X: $i] : (room(X) | ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X))))),
inference(modus_ponens,[status(thm)],[29, 28])).
tff(31,plain,
(![X: $i] : (room(X) | ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X))))),
inference(modus_ponens,[status(thm)],[30, 26])).
tff(32,plain,(
![X: $i] : (room(X) | ((~(old(X) & person(X))) & (~predf(X)) & (~brave(X))))),
inference(skolemize,[status(sab)],[31])).
tff(33,plain,
(![X: $i] : (room(X) | (~(brave(X) | predf(X) | (~((~old(X)) | (~person(X)))))))),
inference(modus_ponens,[status(thm)],[32, 25])).
tff(34,plain,
(![X: $i] : (room(X) | (~(brave(X) | predf(X) | (~((~old(X)) | (~person(X)))))))),
inference(modus_ponens,[status(thm)],[33, 23])).
tff(35,plain,
(((~![X: $i] : (room(X) | (~(brave(X) | predf(X) | (~((~old(X)) | (~person(X)))))))) | (room(X!1) | (~(brave(X!1) | predf(X!1) | (~((~old(X!1)) | (~person(X!1)))))))) <=> ((~![X: $i] : (room(X) | (~(brave(X) | predf(X) | (~((~old(X)) | (~person(X)))))))) | room(X!1) | (~(brave(X!1) | predf(X!1) | (~((~old(X!1)) | (~person(X!1)))))))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
((~![X: $i] : (room(X) | (~(brave(X) | predf(X) | (~((~old(X)) | (~person(X)))))))) | (room(X!1) | (~(brave(X!1) | predf(X!1) | (~((~old(X!1)) | (~person(X!1)))))))),
inference(quant_inst,[status(thm)],[])).
tff(37,plain,
((~![X: $i] : (room(X) | (~(brave(X) | predf(X) | (~((~old(X)) | (~person(X)))))))) | room(X!1) | (~(brave(X!1) | predf(X!1) | (~((~old(X!1)) | (~person(X!1))))))),
inference(modus_ponens,[status(thm)],[36, 35])).
tff(38,plain,
($false),
inference(unit_resolution,[status(thm)],[37, 34, 21, 5])).
tff(39,plain,((~anywhere(X!1)) | (~brave(X!1)) | (~old(X!1)) | (~european(X!1)) | (~((~old(X!1)) | (~european(X!1)) | (~wise(X!1)))) | (~predc(X!1))), inference(lemma,lemma(discharge,[]))).
tff(40,plain,
(((~((~anywhere(X!1)) | (~brave(X!1)) | (~old(X!1)) | (~european(X!1)) | (~((~old(X!1)) | (~european(X!1)) | (~wise(X!1)))) | (~predc(X!1)))) | ![X: $i] : ((~room(X)) | (~((~brave(X)) | (~european(X)) | (~wise(X)))))) <=> ((~((~anywhere(X!1)) | (~brave(X!1)) | (~old(X!1)) | (~european(X!1)) | (~((~old(X!1)) | (~european(X!1)) | (~wise(X!1)))) | (~predc(X!1)))) | ![X: $i] : ((~room(X)) | (~((~brave(X)) | (~european(X)) | (~wise(X))))))),
inference(rewrite,[status(thm)],[])).
tff(41,plain,
(((~((~(brave(X!1) & old(X!1) & european(X!1))) | (~((~(old(X!1) & wise(X!1) & european(X!1))) & predc(X!1))) | (~anywhere(X!1)))) | ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X)))) <=> ((~((~anywhere(X!1)) | (~brave(X!1)) | (~old(X!1)) | (~european(X!1)) | (~((~old(X!1)) | (~european(X!1)) | (~wise(X!1)))) | (~predc(X!1)))) | ![X: $i] : ((~room(X)) | (~((~brave(X)) | (~european(X)) | (~wise(X))))))),
inference(rewrite,[status(thm)],[])).
tff(42,plain,
((~((~(brave(X!1) & old(X!1) & european(X!1))) | (~((~(old(X!1) & wise(X!1) & european(X!1))) & predc(X!1))) | (~anywhere(X!1)))) <=> (~((~(brave(X!1) & old(X!1) & european(X!1))) | (~((~(old(X!1) & wise(X!1) & european(X!1))) & predc(X!1))) | (~anywhere(X!1))))),
inference(rewrite,[status(thm)],[])).
tff(43,plain,
(((~((~(brave(X!1) & old(X!1) & european(X!1))) | (~((~(old(X!1) & wise(X!1) & european(X!1))) & predc(X!1))) | (~anywhere(X!1)))) | ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X)))) <=> ((~((~(brave(X!1) & old(X!1) & european(X!1))) | (~((~(old(X!1) & wise(X!1) & european(X!1))) & predc(X!1))) | (~anywhere(X!1)))) | ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X))))),
inference(monotonicity,[status(thm)],[42])).
tff(44,plain,
(((~![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X)))) | ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X)))) <=> ((~![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X)))) | ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X))))),
inference(rewrite,[status(thm)],[])).
tff(45,plain,
((![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X))) => ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X)))) <=> ((~![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X)))) | ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X))))),
inference(rewrite,[status(thm)],[])).
tff(46,plain,
(^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite(((brave(X) & wise(X)) & european(X)) <=> (brave(X) & wise(X) & european(X))), ((((brave(X) & wise(X)) & european(X)) & (brave(X) & european(X))) <=> ((brave(X) & wise(X) & european(X)) & (brave(X) & european(X))))), rewrite(((brave(X) & wise(X) & european(X)) & (brave(X) & european(X))) <=> (brave(X) & wise(X) & european(X))), ((((brave(X) & wise(X)) & european(X)) & (brave(X) & european(X))) <=> (brave(X) & wise(X) & european(X)))), ((room(X) => (((brave(X) & wise(X)) & european(X)) & (brave(X) & european(X)))) <=> (room(X) => (brave(X) & wise(X) & european(X))))), rewrite((room(X) => (brave(X) & wise(X) & european(X))) <=> ((~room(X)) | (brave(X) & wise(X) & european(X)))), ((room(X) => (((brave(X) & wise(X)) & european(X)) & (brave(X) & european(X)))) <=> ((~room(X)) | (brave(X) & wise(X) & european(X)))))),
inference(bind,[status(th)],[])).
tff(47,plain,
(![X: $i] : (room(X) => (((brave(X) & wise(X)) & european(X)) & (brave(X) & european(X)))) <=> ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X)))),
inference(quant_intro,[status(thm)],[46])).
tff(48,plain,
((~(~![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X))))) <=> ![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X)))),
inference(rewrite,[status(thm)],[])).
tff(49,plain,
((~![X: $i] : (anywhere(X) => (((~((old(X) & wise(X)) & european(X))) & predc(X)) => (~((brave(X) & old(X)) & european(X)))))) <=> (~![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X))))),
inference(rewrite,[status(thm)],[])).
tff(50,plain,
((~(~![X: $i] : (anywhere(X) => (((~((old(X) & wise(X)) & european(X))) & predc(X)) => (~((brave(X) & old(X)) & european(X))))))) <=> (~(~![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X)))))),
inference(monotonicity,[status(thm)],[49])).
tff(51,plain,
((~(~![X: $i] : (anywhere(X) => (((~((old(X) & wise(X)) & european(X))) & predc(X)) => (~((brave(X) & old(X)) & european(X))))))) <=> ![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X)))),
inference(transitivity,[status(thm)],[50, 48])).
tff(52,plain,
(((~(~![X: $i] : (anywhere(X) => (((~((old(X) & wise(X)) & european(X))) & predc(X)) => (~((brave(X) & old(X)) & european(X))))))) => ![X: $i] : (room(X) => (((brave(X) & wise(X)) & european(X)) & (brave(X) & european(X))))) <=> (![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X))) => ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X))))),
inference(monotonicity,[status(thm)],[51, 47])).
tff(53,plain,
(((~(~![X: $i] : (anywhere(X) => (((~((old(X) & wise(X)) & european(X))) & predc(X)) => (~((brave(X) & old(X)) & european(X))))))) => ![X: $i] : (room(X) => (((brave(X) & wise(X)) & european(X)) & (brave(X) & european(X))))) <=> ((~![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X)))) | ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X))))),
inference(transitivity,[status(thm)],[52, 45])).
tff(54,axiom,((~(~![X: $i] : (anywhere(X) => (((~((old(X) & wise(X)) & european(X))) & predc(X)) => (~((brave(X) & old(X)) & european(X))))))) => ![X: $i] : (room(X) => (((brave(X) & wise(X)) & european(X)) & (brave(X) & european(X))))), file('/mnt/tmpfs//1375177612931774584832018.p','p2')).
tff(55,plain,
((~![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X)))) | ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X)))),
inference(modus_ponens,[status(thm)],[54, 53])).
tff(56,plain,
((~![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X)))) | ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X)))),
inference(modus_ponens,[status(thm)],[55, 44])).
tff(57,plain,
((~![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X)))) | ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X)))),
inference(modus_ponens,[status(thm)],[56, 44])).
tff(58,plain,
((~![X: $i] : ((~(brave(X) & old(X) & european(X))) | (~((~(old(X) & wise(X) & european(X))) & predc(X))) | (~anywhere(X)))) | ![X: $i] : ((~room(X)) | (brave(X) & wise(X) & european(X)))),
inference(modus_ponens,[status(thm)],[57, 44])).
|
Brittany, Ray, Nicole, Margaret are the only persons in the room.
If “Nicole is tall, is not creative and is not a rich person” then “someone who is richer than Mary if they is a tall person is older than someone who who is creative is old” otherwise “Nicole is the least quiet in the room”.
Everyone in the room is not a old quiet tall person.
At least one person in the room who is not a quiet person is a rich creative quiet tall person and is not a creative person.
Brittany is the quietest in the room.
Everyone in the room is old. | Brittany is quiet. | entailment | room(brittany)&room(ray)&room(nicole)&room(margaret)&(![X]:(room(X)=>(X='brittany'|X='ray'|X='nicole'|X='margaret')))&
((((((tall(nicole))&(~creative(nicole))&(~(rich(nicole)&person(nicole)))))=>(?[X,Y]:((((tall(X)&person(X))=>(richer(mary,X))))&(((creative(Y))=>(old(Y))))&(older(X,Y)))))|((~(((tall(nicole))&(~creative(nicole))&(~(rich(nicole)&person(nicole))))))=>(![X]:(quieter(nicole,X)))))&
(![X]:(room(X)=>(~(old(X)&quiet(X)&tall(X)&person(X)))))&
(((?[X]:(room(X)&((~(quiet(X)&person(X)))=>(((rich(X)&creative(X)&quiet(X)&tall(X)&person(X))&(~(creative(X)&person(X))))))))))&
(![X]:(quieter(X,brittany)))&
(![X]:(room(X)=>(old(X))))) | room(brittany)&room(ray)&room(nicole)&room(margaret)&(![X]:(room(X)=>(X='brittany'|X='ray'|X='nicole'|X='margaret')))&
(quiet(brittany)) | entailment | [
"p4",
"p5",
"p3",
"p2",
"b13",
"p0",
"hypothesis"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__fred__type, type, (
tptp_fun__fred_: $i)).
tff(tptp_fun__alice__type, type, (
tptp_fun__alice_: $i)).
tff(quiet_type, type, (
quiet: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(quieter_type, type, (
quieter: ( $i * $i ) > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(tall_type, type, (
tall: $i > $o)).
tff(rich_type, type, (
rich: $i > $o)).
tff(creative_type, type, (
creative: $i > $o)).
tff(old_type, type, (
old: $i > $o)).
tff(alice_type, type, (
alice: $i)).
tff(fred_type, type, (
fred: $i)).
tff(paul_type, type, (
paul: $i)).
tff(1,assumption,(~quiet(mary)), introduced(assumption)).
tff(2,plain,
(^[X: $i] : refl(quieter(X, mary) <=> quieter(X, mary))),
inference(bind,[status(th)],[])).
tff(3,plain,
(![X: $i] : quieter(X, mary) <=> ![X: $i] : quieter(X, mary)),
inference(quant_intro,[status(thm)],[2])).
tff(4,plain,
(![X: $i] : quieter(X, mary) <=> ![X: $i] : quieter(X, mary)),
inference(rewrite,[status(thm)],[])).
tff(5,axiom,(![X: $i] : quieter(X, mary)), file('/mnt/tmpfs//2536824461559347022217946.p','p4')).
tff(6,plain,
(![X: $i] : quieter(X, mary)),
inference(modus_ponens,[status(thm)],[5, 4])).
tff(7,plain,(
![X: $i] : quieter(X, mary)),
inference(skolemize,[status(sab)],[6])).
tff(8,plain,
(![X: $i] : quieter(X, mary)),
inference(modus_ponens,[status(thm)],[7, 3])).
tff(9,plain,
((~![X: $i] : quieter(X, mary)) | quieter(X!0, mary)),
inference(quant_inst,[status(thm)],[])).
tff(10,plain,
(quieter(X!0, mary)),
inference(unit_resolution,[status(thm)],[9, 8])).
tff(11,assumption,(~((~quiet(X!0)) | (~person(X!0)) | (~creative(X!0)) | (~((~creative(X!0)) | (~person(X!0)))) | (~rich(X!0)) | (~tall(X!0)))), introduced(assumption)).
tff(12,plain,
(((~quiet(X!0)) | (~person(X!0)) | (~creative(X!0)) | (~((~creative(X!0)) | (~person(X!0)))) | (~rich(X!0)) | (~tall(X!0))) | tall(X!0)),
inference(tautology,[status(thm)],[])).
tff(13,plain,
(tall(X!0)),
inference(unit_resolution,[status(thm)],[12, 11])).
tff(14,plain,
(((~quiet(X!0)) | (~person(X!0)) | (~creative(X!0)) | (~((~creative(X!0)) | (~person(X!0)))) | (~rich(X!0)) | (~tall(X!0))) | quiet(X!0)),
inference(tautology,[status(thm)],[])).
tff(15,plain,
(quiet(X!0)),
inference(unit_resolution,[status(thm)],[14, 11])).
tff(16,plain,
(((~quiet(X!0)) | (~person(X!0)) | (~creative(X!0)) | (~((~creative(X!0)) | (~person(X!0)))) | (~rich(X!0)) | (~tall(X!0))) | person(X!0)),
inference(tautology,[status(thm)],[])).
tff(17,plain,
(person(X!0)),
inference(unit_resolution,[status(thm)],[16, 11])).
tff(18,plain,
(^[X: $i] : refl((old(X) | (~room(X))) <=> (old(X) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(19,plain,
(![X: $i] : (old(X) | (~room(X))) <=> ![X: $i] : (old(X) | (~room(X)))),
inference(quant_intro,[status(thm)],[18])).
tff(20,plain,
(![X: $i] : (old(X) | (~room(X))) <=> ![X: $i] : (old(X) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(21,plain,
(^[X: $i] : rewrite((room(X) => old(X)) <=> (old(X) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(22,plain,
(![X: $i] : (room(X) => old(X)) <=> ![X: $i] : (old(X) | (~room(X)))),
inference(quant_intro,[status(thm)],[21])).
tff(23,axiom,(![X: $i] : (room(X) => old(X))), file('/mnt/tmpfs//2536824461559347022217946.p','p5')).
tff(24,plain,
(![X: $i] : (old(X) | (~room(X)))),
inference(modus_ponens,[status(thm)],[23, 22])).
tff(25,plain,
(![X: $i] : (old(X) | (~room(X)))),
inference(modus_ponens,[status(thm)],[24, 20])).
tff(26,plain,(
![X: $i] : (old(X) | (~room(X)))),
inference(skolemize,[status(sab)],[25])).
tff(27,plain,
(![X: $i] : (old(X) | (~room(X)))),
inference(modus_ponens,[status(thm)],[26, 19])).
tff(28,plain,
(?[X: $i] : (room(X) & ((quiet(X) & person(X)) | (rich(X) & creative(X) & quiet(X) & tall(X) & person(X) & (~(creative(X) & person(X)))))) <=> ?[X: $i] : (room(X) & ((quiet(X) & person(X)) | (rich(X) & creative(X) & quiet(X) & tall(X) & person(X) & (~(creative(X) & person(X))))))),
inference(rewrite,[status(thm)],[])).
tff(29,plain,
(^[X: $i] : rewrite((room(X) & ((~(quiet(X) & person(X))) => (((((rich(X) & creative(X)) & quiet(X)) & tall(X)) & person(X)) & (~(creative(X) & person(X)))))) <=> (room(X) & ((quiet(X) & person(X)) | (rich(X) & creative(X) & quiet(X) & tall(X) & person(X) & (~(creative(X) & person(X)))))))),
inference(bind,[status(th)],[])).
tff(30,plain,
(?[X: $i] : (room(X) & ((~(quiet(X) & person(X))) => (((((rich(X) & creative(X)) & quiet(X)) & tall(X)) & person(X)) & (~(creative(X) & person(X)))))) <=> ?[X: $i] : (room(X) & ((quiet(X) & person(X)) | (rich(X) & creative(X) & quiet(X) & tall(X) & person(X) & (~(creative(X) & person(X))))))),
inference(quant_intro,[status(thm)],[29])).
tff(31,axiom,(?[X: $i] : (room(X) & ((~(quiet(X) & person(X))) => (((((rich(X) & creative(X)) & quiet(X)) & tall(X)) & person(X)) & (~(creative(X) & person(X))))))), file('/mnt/tmpfs//2536824461559347022217946.p','p3')).
tff(32,plain,
(?[X: $i] : (room(X) & ((quiet(X) & person(X)) | (rich(X) & creative(X) & quiet(X) & tall(X) & person(X) & (~(creative(X) & person(X))))))),
inference(modus_ponens,[status(thm)],[31, 30])).
tff(33,plain,
(?[X: $i] : (room(X) & ((quiet(X) & person(X)) | (rich(X) & creative(X) & quiet(X) & tall(X) & person(X) & (~(creative(X) & person(X))))))),
inference(modus_ponens,[status(thm)],[32, 28])).
tff(34,plain,(
room(X!0) & ((quiet(X!0) & person(X!0)) | (rich(X!0) & creative(X!0) & quiet(X!0) & tall(X!0) & person(X!0) & (~(creative(X!0) & person(X!0)))))),
inference(skolemize,[status(sab)],[33])).
tff(35,plain,
(room(X!0)),
inference(and_elim,[status(thm)],[34])).
tff(36,plain,
(((~![X: $i] : (old(X) | (~room(X)))) | (old(X!0) | (~room(X!0)))) <=> ((~![X: $i] : (old(X) | (~room(X)))) | old(X!0) | (~room(X!0)))),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
((~![X: $i] : (old(X) | (~room(X)))) | (old(X!0) | (~room(X!0)))),
inference(quant_inst,[status(thm)],[])).
tff(38,plain,
((~![X: $i] : (old(X) | (~room(X)))) | old(X!0) | (~room(X!0))),
inference(modus_ponens,[status(thm)],[37, 36])).
tff(39,plain,
(old(X!0)),
inference(unit_resolution,[status(thm)],[38, 35, 27])).
tff(40,plain,
(^[X: $i] : refl(((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X))) <=> ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X))))),
inference(bind,[status(th)],[])).
tff(41,plain,
(![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X))) <=> ![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))),
inference(quant_intro,[status(thm)],[40])).
tff(42,plain,
(^[X: $i] : trans(monotonicity(trans(monotonicity(rewrite((old(X) & quiet(X) & tall(X) & person(X)) <=> (~((~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X))))), ((~(old(X) & quiet(X) & tall(X) & person(X))) <=> (~(~((~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X))))))), rewrite((~(~((~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X))))) <=> ((~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))), ((~(old(X) & quiet(X) & tall(X) & person(X))) <=> ((~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X))))), (((~room(X)) | (~(old(X) & quiet(X) & tall(X) & person(X)))) <=> ((~room(X)) | ((~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))))), rewrite(((~room(X)) | ((~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))) <=> ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))), (((~room(X)) | (~(old(X) & quiet(X) & tall(X) & person(X)))) <=> ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))))),
inference(bind,[status(th)],[])).
tff(43,plain,
(![X: $i] : ((~room(X)) | (~(old(X) & quiet(X) & tall(X) & person(X)))) <=> ![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))),
inference(quant_intro,[status(thm)],[42])).
tff(44,plain,
(![X: $i] : ((~room(X)) | (~(old(X) & quiet(X) & tall(X) & person(X)))) <=> ![X: $i] : ((~room(X)) | (~(old(X) & quiet(X) & tall(X) & person(X))))),
inference(rewrite,[status(thm)],[])).
tff(45,plain,
(^[X: $i] : trans(monotonicity(rewrite((~(((old(X) & quiet(X)) & tall(X)) & person(X))) <=> (~(old(X) & quiet(X) & tall(X) & person(X)))), ((room(X) => (~(((old(X) & quiet(X)) & tall(X)) & person(X)))) <=> (room(X) => (~(old(X) & quiet(X) & tall(X) & person(X)))))), rewrite((room(X) => (~(old(X) & quiet(X) & tall(X) & person(X)))) <=> ((~room(X)) | (~(old(X) & quiet(X) & tall(X) & person(X))))), ((room(X) => (~(((old(X) & quiet(X)) & tall(X)) & person(X)))) <=> ((~room(X)) | (~(old(X) & quiet(X) & tall(X) & person(X))))))),
inference(bind,[status(th)],[])).
tff(46,plain,
(![X: $i] : (room(X) => (~(((old(X) & quiet(X)) & tall(X)) & person(X)))) <=> ![X: $i] : ((~room(X)) | (~(old(X) & quiet(X) & tall(X) & person(X))))),
inference(quant_intro,[status(thm)],[45])).
tff(47,axiom,(![X: $i] : (room(X) => (~(((old(X) & quiet(X)) & tall(X)) & person(X))))), file('/mnt/tmpfs//2536824461559347022217946.p','p2')).
tff(48,plain,
(![X: $i] : ((~room(X)) | (~(old(X) & quiet(X) & tall(X) & person(X))))),
inference(modus_ponens,[status(thm)],[47, 46])).
tff(49,plain,
(![X: $i] : ((~room(X)) | (~(old(X) & quiet(X) & tall(X) & person(X))))),
inference(modus_ponens,[status(thm)],[48, 44])).
tff(50,plain,(
![X: $i] : ((~room(X)) | (~(old(X) & quiet(X) & tall(X) & person(X))))),
inference(skolemize,[status(sab)],[49])).
tff(51,plain,
(![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))),
inference(modus_ponens,[status(thm)],[50, 43])).
tff(52,plain,
(![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))),
inference(modus_ponens,[status(thm)],[51, 41])).
tff(53,plain,
(((~![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))) | ((~quiet(X!0)) | (~person(X!0)) | (~tall(X!0)) | (~room(X!0)) | (~old(X!0)))) <=> ((~![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))) | (~quiet(X!0)) | (~person(X!0)) | (~tall(X!0)) | (~room(X!0)) | (~old(X!0)))),
inference(rewrite,[status(thm)],[])).
tff(54,plain,
(((~room(X!0)) | (~old(X!0)) | (~quiet(X!0)) | (~tall(X!0)) | (~person(X!0))) <=> ((~quiet(X!0)) | (~person(X!0)) | (~tall(X!0)) | (~room(X!0)) | (~old(X!0)))),
inference(rewrite,[status(thm)],[])).
tff(55,plain,
(((~![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))) | ((~room(X!0)) | (~old(X!0)) | (~quiet(X!0)) | (~tall(X!0)) | (~person(X!0)))) <=> ((~![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))) | ((~quiet(X!0)) | (~person(X!0)) | (~tall(X!0)) | (~room(X!0)) | (~old(X!0))))),
inference(monotonicity,[status(thm)],[54])).
tff(56,plain,
(((~![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))) | ((~room(X!0)) | (~old(X!0)) | (~quiet(X!0)) | (~tall(X!0)) | (~person(X!0)))) <=> ((~![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))) | (~quiet(X!0)) | (~person(X!0)) | (~tall(X!0)) | (~room(X!0)) | (~old(X!0)))),
inference(transitivity,[status(thm)],[55, 53])).
tff(57,plain,
((~![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))) | ((~room(X!0)) | (~old(X!0)) | (~quiet(X!0)) | (~tall(X!0)) | (~person(X!0)))),
inference(quant_inst,[status(thm)],[])).
tff(58,plain,
((~![X: $i] : ((~room(X)) | (~old(X)) | (~quiet(X)) | (~tall(X)) | (~person(X)))) | (~quiet(X!0)) | (~person(X!0)) | (~tall(X!0)) | (~room(X!0)) | (~old(X!0))),
inference(modus_ponens,[status(thm)],[57, 56])).
tff(59,plain,
((~quiet(X!0)) | (~person(X!0)) | (~tall(X!0))),
inference(unit_resolution,[status(thm)],[58, 52, 35, 39])).
tff(60,plain,
($false),
inference(unit_resolution,[status(thm)],[59, 17, 15, 13])).
tff(61,plain,((~quiet(X!0)) | (~person(X!0)) | (~creative(X!0)) | (~((~creative(X!0)) | (~person(X!0)))) | (~rich(X!0)) | (~tall(X!0))), inference(lemma,lemma(discharge,[]))).
tff(62,plain,
(((quiet(X!0) & person(X!0)) | (rich(X!0) & creative(X!0) & quiet(X!0) & tall(X!0) & person(X!0) & (~(creative(X!0) & person(X!0))))) <=> ((~((~quiet(X!0)) | (~person(X!0)))) | (~((~quiet(X!0)) | (~person(X!0)) | (~creative(X!0)) | (~((~creative(X!0)) | (~person(X!0)))) | (~rich(X!0)) | (~tall(X!0)))))),
inference(rewrite,[status(thm)],[])).
tff(63,plain,
((quiet(X!0) & person(X!0)) | (rich(X!0) & creative(X!0) & quiet(X!0) & tall(X!0) & person(X!0) & (~(creative(X!0) & person(X!0))))),
inference(and_elim,[status(thm)],[34])).
tff(64,plain,
((~((~quiet(X!0)) | (~person(X!0)))) | (~((~quiet(X!0)) | (~person(X!0)) | (~creative(X!0)) | (~((~creative(X!0)) | (~person(X!0)))) | (~rich(X!0)) | (~tall(X!0))))),
inference(modus_ponens,[status(thm)],[63, 62])).
tff(65,plain,
(~((~quiet(X!0)) | (~person(X!0)))),
inference(unit_resolution,[status(thm)],[64, 61])).
tff(66,plain,
(((~quiet(X!0)) | (~person(X!0))) | quiet(X!0)),
inference(tautology,[status(thm)],[])).
tff(67,plain,
(quiet(X!0)),
inference(unit_resolution,[status(thm)],[66, 65])).
tff(68,plain,
(^[X: $i, Y: $i] : refl(((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X))) <=> ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X))))),
inference(bind,[status(th)],[])).
tff(69,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X))) <=> ![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))),
inference(quant_intro,[status(thm)],[68])).
tff(70,plain,
(^[X: $i, Y: $i] : trans(monotonicity(trans(monotonicity(rewrite((quieter(X, Y) & quiet(X)) <=> (~((~quieter(X, Y)) | (~quiet(X))))), ((~(quieter(X, Y) & quiet(X))) <=> (~(~((~quieter(X, Y)) | (~quiet(X))))))), rewrite((~(~((~quieter(X, Y)) | (~quiet(X))))) <=> ((~quieter(X, Y)) | (~quiet(X)))), ((~(quieter(X, Y) & quiet(X))) <=> ((~quieter(X, Y)) | (~quiet(X))))), (((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X)))) <=> ((X = Y) | quiet(Y) | ((~quieter(X, Y)) | (~quiet(X)))))), rewrite(((X = Y) | quiet(Y) | ((~quieter(X, Y)) | (~quiet(X)))) <=> ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))), (((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X)))) <=> ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))))),
inference(bind,[status(th)],[])).
tff(71,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X)))) <=> ![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))),
inference(quant_intro,[status(thm)],[70])).
tff(72,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X)))) <=> ![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(rewrite,[status(thm)],[])).
tff(73,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite(((quieter(X, Y) & quiet(X)) => quiet(Y)) <=> (quiet(Y) | (~(quieter(X, Y) & quiet(X))))), (((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y))) <=> ((~(X = Y)) => (quiet(Y) | (~(quieter(X, Y) & quiet(X))))))), rewrite(((~(X = Y)) => (quiet(Y) | (~(quieter(X, Y) & quiet(X))))) <=> ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))), (((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y))) <=> ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))))),
inference(bind,[status(th)],[])).
tff(74,plain,
(![X: $i, Y: $i] : ((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y))) <=> ![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(quant_intro,[status(thm)],[73])).
tff(75,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => ((quieter(X, Y) & quiet(X)) => quiet(Y)))), file('/mnt/tmpfs//2536824461559347022217946.p','b13')).
tff(76,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(modus_ponens,[status(thm)],[75, 74])).
tff(77,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(modus_ponens,[status(thm)],[76, 72])).
tff(78,plain,(
![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~(quieter(X, Y) & quiet(X))))),
inference(skolemize,[status(sab)],[77])).
tff(79,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))),
inference(modus_ponens,[status(thm)],[78, 71])).
tff(80,plain,
(![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))),
inference(modus_ponens,[status(thm)],[79, 69])).
tff(81,plain,
(((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | (quiet(mary) | (~quiet(X!0)) | (X!0 = mary) | (~quieter(X!0, mary)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | quiet(mary) | (~quiet(X!0)) | (X!0 = mary) | (~quieter(X!0, mary)))),
inference(rewrite,[status(thm)],[])).
tff(82,plain,
(((X!0 = mary) | quiet(mary) | (~quieter(X!0, mary)) | (~quiet(X!0))) <=> (quiet(mary) | (~quiet(X!0)) | (X!0 = mary) | (~quieter(X!0, mary)))),
inference(rewrite,[status(thm)],[])).
tff(83,plain,
(((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | ((X!0 = mary) | quiet(mary) | (~quieter(X!0, mary)) | (~quiet(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | (quiet(mary) | (~quiet(X!0)) | (X!0 = mary) | (~quieter(X!0, mary))))),
inference(monotonicity,[status(thm)],[82])).
tff(84,plain,
(((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | ((X!0 = mary) | quiet(mary) | (~quieter(X!0, mary)) | (~quiet(X!0)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | quiet(mary) | (~quiet(X!0)) | (X!0 = mary) | (~quieter(X!0, mary)))),
inference(transitivity,[status(thm)],[83, 81])).
tff(85,plain,
((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | ((X!0 = mary) | quiet(mary) | (~quieter(X!0, mary)) | (~quiet(X!0)))),
inference(quant_inst,[status(thm)],[])).
tff(86,plain,
((~![X: $i, Y: $i] : ((X = Y) | quiet(Y) | (~quieter(X, Y)) | (~quiet(X)))) | quiet(mary) | (~quiet(X!0)) | (X!0 = mary) | (~quieter(X!0, mary))),
inference(modus_ponens,[status(thm)],[85, 84])).
tff(87,plain,
(quiet(mary) | (X!0 = mary)),
inference(unit_resolution,[status(thm)],[86, 80, 67, 10])).
tff(88,plain,
(X!0 = mary),
inference(unit_resolution,[status(thm)],[87, 1])).
tff(89,plain,
(quiet(X!0) <=> quiet(mary)),
inference(monotonicity,[status(thm)],[88])).
tff(90,plain,
(quiet(mary) <=> quiet(X!0)),
inference(symmetry,[status(thm)],[89])).
tff(91,plain,
((~quiet(mary)) <=> (~quiet(X!0))),
inference(monotonicity,[status(thm)],[90])).
tff(92,plain,
(~quiet(X!0)),
inference(modus_ponens,[status(thm)],[1, 91])).
tff(93,plain,
($false),
inference(unit_resolution,[status(thm)],[67, 92])).
tff(94,plain,(quiet(mary)), inference(lemma,lemma(discharge,[]))).
tff(95,plain,
(room(alice) <=> room(alice)),
inference(rewrite,[status(thm)],[])).
tff(96,axiom,((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))), file('/mnt/tmpfs//2536824461559347022217946.p','p0')).
tff(97,plain,
(((room(mary) & room(paul)) & room(fred)) & room(alice)),
inference(and_elim,[status(thm)],[96])).
tff(98,plain,
(room(alice)),
inference(and_elim,[status(thm)],[97])).
tff(99,plain,
(room(alice)),
inference(modus_ponens,[status(thm)],[98, 95])).
tff(100,plain,
(room(fred) <=> room(fred)),
inference(rewrite,[status(thm)],[])).
tff(101,plain,
((room(mary) & room(paul)) & room(fred)),
inference(and_elim,[status(thm)],[97])).
tff(102,plain,
(room(fred)),
inference(and_elim,[status(thm)],[101])).
tff(103,plain,
(room(fred)),
inference(modus_ponens,[status(thm)],[102, 100])).
tff(104,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(105,plain,
(room(mary) & room(paul)),
inference(and_elim,[status(thm)],[101])).
tff(106,plain,
(room(paul)),
inference(and_elim,[status(thm)],[105])).
tff(107,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[106, 104])).
tff(108,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(109,plain,
(room(mary)),
inference(and_elim,[status(thm)],[105])).
tff(110,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[109, 108])).
tff(111,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~quiet(mary))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~quiet(mary)))),
inference(rewrite,[status(thm)],[])).
tff(112,plain,
((~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))),
inference(rewrite,[status(thm)],[])).
tff(113,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~quiet(mary))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~quiet(mary)))),
inference(monotonicity,[status(thm)],[112])).
tff(114,plain,
(((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~quiet(mary))) <=> ((~room(mary)) | (~room(paul)) | (~room(fred)) | (~room(alice)) | (~((X!1 = |'alice'|) | (X!1 = |'fred'|) | (X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~quiet(mary)))),
inference(transitivity,[status(thm)],[113, 111])).
tff(115,plain,
((room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quiet(mary)) <=> (room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quiet(mary))),
inference(rewrite,[status(thm)],[])).
tff(116,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quiet(mary))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quiet(mary)))),
inference(monotonicity,[status(thm)],[115])).
tff(117,plain,
((~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quiet(mary))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quiet(mary)))),
inference(rewrite,[status(thm)],[])).
tff(118,plain,
((~(((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & quiet(mary))) <=> (~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quiet(mary)))),
inference(rewrite,[status(thm)],[])).
tff(119,axiom,(~(((((room(mary) & room(paul)) & room(fred)) & room(alice)) & ![X: $i] : (room(X) => ((((X = |'mary'|) | (X = |'paul'|)) | (X = |'fred'|)) | (X = |'alice'|)))) & quiet(mary))), file('/mnt/tmpfs//2536824461559347022217946.p','hypothesis')).
tff(120,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quiet(mary))),
inference(modus_ponens,[status(thm)],[119, 118])).
tff(121,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quiet(mary))),
inference(modus_ponens,[status(thm)],[120, 116])).
tff(122,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quiet(mary))),
inference(modus_ponens,[status(thm)],[121, 117])).
tff(123,plain,
(~(room(mary) & room(paul) & room(fred) & room(alice) & ![X: $i] : ((X = |'alice'|) | (X = |'fred'|) | (X = |'paul'|) | (X = |'mary'|) | (~room(X))) & quiet(mary))),
inference(modus_ponens,[status(thm)],[122, 116])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (refl (~ (not (room fred)) (not (room fred)))))
(a!4 (refl (~ (not (room alice)) (not (room alice)))))
(a!5 (forall ((X $i))
(or (= X |'alice'|)
(= X |'fred'|)
(= X |'paul'|)
(= X |'mary'|)
(not (room X)))))
(a!6 (not (or (= X!1 |'alice'|)
(= X!1 |'fred'|)
(= X!1 |'paul'|)
(= X!1 |'mary'|)
(not (room X!1)))))
(a!7 (refl (~ (not (quiet mary)) (not (quiet mary))))))
(let ((a!8 (~ (not (and (room mary)
(room paul)
(room fred)
(room alice)
a!5
(quiet mary)))
(or (not (room mary))
(not (room paul))
(not (room fred))
(not (room alice))
a!6
(not (quiet mary))))))
(nnf-neg a!1 a!2 a!3 a!4 (sk (~ (not a!5) a!6)) a!7 a!8)))
|
Cedric is the only person in the room. “Cedric is a happy person” if “not everyone anywhere who either is a quiet person or is wise but not both either is older than Lakeshia or is quiet but not both”. Everyone outside the room is old. Cedric is a brave wise old happy person. Cedric is a happy person. | Cedric is a wise person and is wise. | entailment | room(cedric)&(![X]:(room(X)=>(X='cedric')))&
(((~![X]:(anywhere(X)=>(((((quiet(X)&person(X))<~>(wise(X))))=>(((older(lakeshia,X))<~>(quiet(X))))))))=>(happy(cedric)&person(cedric)))&
(![X]:(~room(X)=>(old(X))))&
(brave(cedric)&wise(cedric)&old(cedric)&happy(cedric)&person(cedric))&
(happy(cedric)&person(cedric))) | room(cedric)&(![X]:(room(X)=>(X='cedric')))&
(((wise(cedric)&person(cedric))&(wise(cedric)))) | contradiction | [
"p3",
"p0",
"hypothesis"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(wise_type, type, (
wise: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(brave_type, type, (
brave: $i > $o)).
tff(old_type, type, (
old: $i > $o)).
tff(happy_type, type, (
happy: $i > $o)).
tff(person_type, type, (
person: $i > $o)).
tff(1,plain,
(wise(mary) <=> wise(mary)),
inference(rewrite,[status(thm)],[])).
tff(2,axiom,((((brave(mary) & wise(mary)) & old(mary)) & happy(mary)) & person(mary)), file('/mnt/tmpfs//148076556553224816890079.p','p3')).
tff(3,plain,
(((brave(mary) & wise(mary)) & old(mary)) & happy(mary)),
inference(and_elim,[status(thm)],[2])).
tff(4,plain,
((brave(mary) & wise(mary)) & old(mary)),
inference(and_elim,[status(thm)],[3])).
tff(5,plain,
(brave(mary) & wise(mary)),
inference(and_elim,[status(thm)],[4])).
tff(6,plain,
(wise(mary)),
inference(and_elim,[status(thm)],[5])).
tff(7,plain,
(wise(mary)),
inference(modus_ponens,[status(thm)],[6, 1])).
tff(8,plain,
(person(mary) <=> person(mary)),
inference(rewrite,[status(thm)],[])).
tff(9,plain,
(person(mary)),
inference(and_elim,[status(thm)],[2])).
tff(10,plain,
(person(mary)),
inference(modus_ponens,[status(thm)],[9, 8])).
tff(11,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(12,axiom,(room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))), file('/mnt/tmpfs//148076556553224816890079.p','p0')).
tff(13,plain,
(room(mary)),
inference(and_elim,[status(thm)],[12])).
tff(14,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[13, 11])).
tff(15,plain,
(((~room(mary)) | (~((~room(X!0)) | (X!0 = |'mary'|))) | (~wise(mary)) | (~person(mary))) <=> ((~room(mary)) | (~((~room(X!0)) | (X!0 = |'mary'|))) | (~wise(mary)) | (~person(mary)))),
inference(rewrite,[status(thm)],[])).
tff(16,plain,
((room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & wise(mary) & person(mary)) <=> (room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & wise(mary) & person(mary))),
inference(rewrite,[status(thm)],[])).
tff(17,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & wise(mary) & person(mary))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & wise(mary) & person(mary)))),
inference(monotonicity,[status(thm)],[16])).
tff(18,plain,
((~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & wise(mary) & person(mary))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & wise(mary) & person(mary)))),
inference(rewrite,[status(thm)],[])).
tff(19,plain,
((~((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((wise(mary) & person(mary)) & wise(mary)))) <=> (~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & wise(mary) & person(mary)))),
inference(rewrite,[status(thm)],[])).
tff(20,axiom,(~((room(mary) & ![X: $i] : (room(X) => (X = |'mary'|))) & ((wise(mary) & person(mary)) & wise(mary)))), file('/mnt/tmpfs//148076556553224816890079.p','hypothesis')).
tff(21,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & wise(mary) & person(mary))),
inference(modus_ponens,[status(thm)],[20, 19])).
tff(22,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & wise(mary) & person(mary))),
inference(modus_ponens,[status(thm)],[21, 17])).
tff(23,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & wise(mary) & person(mary))),
inference(modus_ponens,[status(thm)],[22, 18])).
tff(24,plain,
(~(room(mary) & ![X: $i] : ((~room(X)) | (X = |'mary'|)) & wise(mary) & person(mary))),
inference(modus_ponens,[status(thm)],[23, 17])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (forall ((X $i)) (or (not (room X)) (= X |'mary'|))))
(a!3 (not (or (not (room X!0)) (= X!0 |'mary'|))))
(a!4 (refl (~ (not (wise mary)) (not (wise mary)))))
(a!5 (refl (~ (not (person mary)) (not (person mary))))))
(let ((a!6 (~ (not (and (room mary) a!2 (wise mary) (person mary)))
(or (not (room mary)) a!3 (not (wise mary)) (not (person mary))))))
(nnf-neg a!1 (sk (~ (not a!2) a!3)) a!4 a!5 a!6)))
|
Ralph, Terry are the only persons in the room.
It is not the case that “everyone in the room bakes bread at home if they does not bake bread at home, is older than Juli and is a old person”.
Juli is older than Terry.
Ralph does not bake bread at home, bakes bread at home and is older than Richard if he/she either bakes bread at home or is not old but not both. | Ralph is older than Juli. | entailment | room(ralph)&room(terry)&(![X]:(room(X)=>(X='ralph'|X='terry')))&
((~(![X]:(room(X)=>(((((does_not_bake_bread_at_home(X))&(older(juli,X))&(old(X)&person(X))))=>(bakes_bread_at_home(X)))))))&
(older(terry,juli))&
(((((bakes_bread_at_home(ralph))<~>(~old(ralph))))=>(((does_not_bake_bread_at_home(ralph))&(bakes_bread_at_home(ralph))&(older(richard,ralph))))))) | room(ralph)&room(terry)&(![X]:(room(X)=>(X='ralph'|X='terry')))&
(older(juli,ralph)) | contradiction | [
"p1",
"b18",
"p2",
"b17",
"p0",
"hypothesis"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_1_type, type, (
tptp_fun_X_1: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(older_type, type, (
older: ( $i * $i ) > $o)).
tff(mary_type, type, (
mary: $i)).
tff(fred_type, type, (
fred: $i)).
tff(tptp_fun_X_0_type, type, (
tptp_fun_X_0: $i)).
tff(paul_type, type, (
paul: $i)).
tff(person_type, type, (
person: $i > $o)).
tff(old_type, type, (
old: $i > $o)).
tff(prede_type, type, (
prede: $i > $o)).
tff(lucy_type, type, (
lucy: $i)).
tff(susan_type, type, (
susan: $i)).
tff(john_type, type, (
john: $i)).
tff(alice_type, type, (
alice: $i)).
tff(1,assumption,(~older(fred, mary)), introduced(assumption)).
tff(2,assumption,(X!0 = |'paul'|), introduced(assumption)).
tff(3,plain,
(|'paul'| = X!0),
inference(symmetry,[status(thm)],[2])).
tff(4,plain,
(older(fred, |'paul'|) <=> older(fred, X!0)),
inference(monotonicity,[status(thm)],[3])).
tff(5,plain,
(older(fred, X!0) <=> older(fred, |'paul'|)),
inference(symmetry,[status(thm)],[4])).
tff(6,plain,
((~![X: $i] : (prede(X) | (~room(X)) | (~((~prede(X)) & older(fred, X) & old(X) & person(X))))) <=> (~![X: $i] : (prede(X) | (~room(X)) | (~((~prede(X)) & older(fred, X) & old(X) & person(X)))))),
inference(rewrite,[status(thm)],[])).
tff(7,plain,
((~![X: $i] : (room(X) => ((((~prede(X)) & older(fred, X)) & (old(X) & person(X))) => prede(X)))) <=> (~![X: $i] : (prede(X) | (~room(X)) | (~((~prede(X)) & older(fred, X) & old(X) & person(X)))))),
inference(rewrite,[status(thm)],[])).
tff(8,axiom,(~![X: $i] : (room(X) => ((((~prede(X)) & older(fred, X)) & (old(X) & person(X))) => prede(X)))), file('/mnt/tmpfs//393391041369572684458198.p','p1')).
tff(9,plain,
(~![X: $i] : (prede(X) | (~room(X)) | (~((~prede(X)) & older(fred, X) & old(X) & person(X))))),
inference(modus_ponens,[status(thm)],[8, 7])).
tff(10,plain,
(~![X: $i] : (prede(X) | (~room(X)) | (~((~prede(X)) & older(fred, X) & old(X) & person(X))))),
inference(modus_ponens,[status(thm)],[9, 6])).
tff(11,plain,
(~![X: $i] : (prede(X) | (~room(X)) | (~((~prede(X)) & older(fred, X) & old(X) & person(X))))),
inference(modus_ponens,[status(thm)],[10, 6])).
tff(12,plain,
(~![X: $i] : (prede(X) | (~room(X)) | (~((~prede(X)) & older(fred, X) & old(X) & person(X))))),
inference(modus_ponens,[status(thm)],[11, 6])).
tff(13,plain,(
~(prede(X!0) | (~room(X!0)) | (~((~prede(X!0)) & older(fred, X!0) & old(X!0) & person(X!0))))),
inference(skolemize,[status(sab)],[12])).
tff(14,plain,
((~prede(X!0)) & older(fred, X!0) & old(X!0) & person(X!0)),
inference(or_elim,[status(thm)],[13])).
tff(15,plain,
(older(fred, X!0)),
inference(and_elim,[status(thm)],[14])).
tff(16,plain,
(older(fred, |'paul'|)),
inference(modus_ponens,[status(thm)],[15, 5])).
tff(17,plain,
((fred = paul) <=> (paul = fred)),
inference(commutativity,[status(thm)],[])).
tff(18,assumption,(paul = |'paul'|), introduced(assumption)).
tff(19,plain,
(|'paul'| = paul),
inference(symmetry,[status(thm)],[18])).
tff(20,plain,
((fred = |'paul'|) <=> (fred = paul)),
inference(monotonicity,[status(thm)],[19])).
tff(21,plain,
((fred = |'paul'|) <=> (paul = fred)),
inference(transitivity,[status(thm)],[20, 17])).
tff(22,plain,
((paul = fred) <=> (fred = |'paul'|)),
inference(symmetry,[status(thm)],[21])).
tff(23,plain,
((~(paul = fred)) <=> (~(fred = |'paul'|))),
inference(monotonicity,[status(thm)],[22])).
tff(24,plain,
((~(paul = fred)) <=> (~(paul = fred))),
inference(rewrite,[status(thm)],[])).
tff(25,axiom,((((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))) & (~(lucy = susan))), file('/mnt/tmpfs//393391041369572684458198.p','b18')).
tff(26,plain,
(((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))) & (~(lucy = john))),
inference(and_elim,[status(thm)],[25])).
tff(27,plain,
((((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))) & (~(lucy = alice))),
inference(and_elim,[status(thm)],[26])).
tff(28,plain,
(((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))) & (~(lucy = fred))),
inference(and_elim,[status(thm)],[27])).
tff(29,plain,
((((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))) & (~(lucy = paul))),
inference(and_elim,[status(thm)],[28])).
tff(30,plain,
(((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))) & (~(lucy = mary))),
inference(and_elim,[status(thm)],[29])).
tff(31,plain,
((((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))) & (~(susan = lucy))),
inference(and_elim,[status(thm)],[30])).
tff(32,plain,
(((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))) & (~(susan = john))),
inference(and_elim,[status(thm)],[31])).
tff(33,plain,
((((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))) & (~(susan = alice))),
inference(and_elim,[status(thm)],[32])).
tff(34,plain,
(((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))) & (~(susan = fred))),
inference(and_elim,[status(thm)],[33])).
tff(35,plain,
((((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))) & (~(susan = paul))),
inference(and_elim,[status(thm)],[34])).
tff(36,plain,
(((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))) & (~(susan = mary))),
inference(and_elim,[status(thm)],[35])).
tff(37,plain,
((((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))) & (~(john = lucy))),
inference(and_elim,[status(thm)],[36])).
tff(38,plain,
(((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))) & (~(john = susan))),
inference(and_elim,[status(thm)],[37])).
tff(39,plain,
((((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))) & (~(john = alice))),
inference(and_elim,[status(thm)],[38])).
tff(40,plain,
(((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))) & (~(john = fred))),
inference(and_elim,[status(thm)],[39])).
tff(41,plain,
((((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))) & (~(john = paul))),
inference(and_elim,[status(thm)],[40])).
tff(42,plain,
(((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))) & (~(john = mary))),
inference(and_elim,[status(thm)],[41])).
tff(43,plain,
((((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))) & (~(alice = lucy))),
inference(and_elim,[status(thm)],[42])).
tff(44,plain,
(((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))) & (~(alice = susan))),
inference(and_elim,[status(thm)],[43])).
tff(45,plain,
((((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))) & (~(alice = john))),
inference(and_elim,[status(thm)],[44])).
tff(46,plain,
(((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))) & (~(alice = fred))),
inference(and_elim,[status(thm)],[45])).
tff(47,plain,
((((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))) & (~(alice = paul))),
inference(and_elim,[status(thm)],[46])).
tff(48,plain,
(((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))) & (~(alice = mary))),
inference(and_elim,[status(thm)],[47])).
tff(49,plain,
((((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))) & (~(fred = lucy))),
inference(and_elim,[status(thm)],[48])).
tff(50,plain,
(((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))) & (~(fred = susan))),
inference(and_elim,[status(thm)],[49])).
tff(51,plain,
((((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))) & (~(fred = john))),
inference(and_elim,[status(thm)],[50])).
tff(52,plain,
(((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))) & (~(fred = alice))),
inference(and_elim,[status(thm)],[51])).
tff(53,plain,
((((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))) & (~(fred = paul))),
inference(and_elim,[status(thm)],[52])).
tff(54,plain,
(((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))) & (~(fred = mary))),
inference(and_elim,[status(thm)],[53])).
tff(55,plain,
((((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))) & (~(paul = lucy))),
inference(and_elim,[status(thm)],[54])).
tff(56,plain,
(((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))) & (~(paul = susan))),
inference(and_elim,[status(thm)],[55])).
tff(57,plain,
((((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))) & (~(paul = john))),
inference(and_elim,[status(thm)],[56])).
tff(58,plain,
(((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))) & (~(paul = alice))),
inference(and_elim,[status(thm)],[57])).
tff(59,plain,
((((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))) & (~(paul = fred))),
inference(and_elim,[status(thm)],[58])).
tff(60,plain,
(~(paul = fred)),
inference(and_elim,[status(thm)],[59])).
tff(61,plain,
(~(paul = fred)),
inference(modus_ponens,[status(thm)],[60, 24])).
tff(62,plain,
(~(fred = |'paul'|)),
inference(modus_ponens,[status(thm)],[61, 23])).
tff(63,plain,
(older(|'paul'|, fred) <=> older(paul, fred)),
inference(monotonicity,[status(thm)],[19])).
tff(64,plain,
(older(paul, fred) <=> older(|'paul'|, fred)),
inference(symmetry,[status(thm)],[63])).
tff(65,plain,
(older(paul, fred) <=> older(paul, fred)),
inference(rewrite,[status(thm)],[])).
tff(66,axiom,(older(paul, fred)), file('/mnt/tmpfs//393391041369572684458198.p','p2')).
tff(67,plain,
(older(paul, fred)),
inference(modus_ponens,[status(thm)],[66, 65])).
tff(68,plain,
(older(|'paul'|, fred)),
inference(modus_ponens,[status(thm)],[67, 64])).
tff(69,plain,
(![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(70,plain,
(![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y))) <=> ![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))),
inference(rewrite,[status(thm)],[])).
tff(71,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite((older(X, Y) => (~older(Y, X))) <=> ((~older(Y, X)) | (~older(X, Y)))), (((~(X = Y)) => (older(X, Y) => (~older(Y, X)))) <=> ((~(X = Y)) => ((~older(Y, X)) | (~older(X, Y)))))), rewrite(((~(X = Y)) => ((~older(Y, X)) | (~older(X, Y)))) <=> ((X = Y) | (~older(Y, X)) | (~older(X, Y)))), (((~(X = Y)) => (older(X, Y) => (~older(Y, X)))) <=> ((X = Y) | (~older(Y, X)) | (~older(X, Y)))))),
inference(bind,[status(th)],[])).
tff(72,plain,
(![X: $i, Y: $i] : ((~(X = Y)) => (older(X, Y) => (~older(Y, X)))) <=> ![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))),
inference(quant_intro,[status(thm)],[71])).
tff(73,axiom,(![X: $i, Y: $i] : ((~(X = Y)) => (older(X, Y) => (~older(Y, X))))), file('/mnt/tmpfs//393391041369572684458198.p','b17')).
tff(74,plain,
(![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))),
inference(modus_ponens,[status(thm)],[73, 72])).
tff(75,plain,
(![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))),
inference(modus_ponens,[status(thm)],[74, 70])).
tff(76,plain,(
![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))),
inference(skolemize,[status(sab)],[75])).
tff(77,plain,
(![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))),
inference(modus_ponens,[status(thm)],[76, 69])).
tff(78,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))) | ((fred = |'paul'|) | (~older(|'paul'|, fred)) | (~older(fred, |'paul'|)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))) | (fred = |'paul'|) | (~older(|'paul'|, fred)) | (~older(fred, |'paul'|)))),
inference(rewrite,[status(thm)],[])).
tff(79,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))) | ((fred = |'paul'|) | (~older(|'paul'|, fred)) | (~older(fred, |'paul'|)))),
inference(quant_inst,[status(thm)],[])).
tff(80,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))) | (fred = |'paul'|) | (~older(|'paul'|, fred)) | (~older(fred, |'paul'|))),
inference(modus_ponens,[status(thm)],[79, 78])).
tff(81,plain,
((fred = |'paul'|) | (~older(|'paul'|, fred)) | (~older(fred, |'paul'|))),
inference(unit_resolution,[status(thm)],[80, 77])).
tff(82,plain,
($false),
inference(unit_resolution,[status(thm)],[81, 68, 62, 16])).
tff(83,plain,((~(paul = |'paul'|)) | (~(X!0 = |'paul'|))), inference(lemma,lemma(discharge,[]))).
tff(84,plain,
(~(paul = |'paul'|)),
inference(unit_resolution,[status(thm)],[83, 2])).
tff(85,plain,
(^[X: $i] : refl(((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(86,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[85])).
tff(87,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(88,plain,
(^[X: $i] : rewrite((room(X) => ((X = |'mary'|) | (X = |'paul'|))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(89,plain,
(![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[88])).
tff(90,axiom,((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))), file('/mnt/tmpfs//393391041369572684458198.p','p0')).
tff(91,plain,
(![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))),
inference(and_elim,[status(thm)],[90])).
tff(92,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[91, 89])).
tff(93,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[92, 87])).
tff(94,plain,(
![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[93])).
tff(95,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[94, 86])).
tff(96,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(97,plain,
(room(mary) & room(paul)),
inference(and_elim,[status(thm)],[90])).
tff(98,plain,
(room(paul)),
inference(and_elim,[status(thm)],[97])).
tff(99,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[98, 96])).
tff(100,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(101,plain,
(((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul))) <=> ((~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(102,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|)))),
inference(monotonicity,[status(thm)],[101])).
tff(103,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|))),
inference(transitivity,[status(thm)],[102, 100])).
tff(104,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((paul = |'paul'|) | (paul = |'mary'|) | (~room(paul)))),
inference(quant_inst,[status(thm)],[])).
tff(105,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(paul)) | (paul = |'paul'|) | (paul = |'mary'|)),
inference(modus_ponens,[status(thm)],[104, 103])).
tff(106,plain,
((paul = |'paul'|) | (paul = |'mary'|)),
inference(unit_resolution,[status(thm)],[105, 99, 95])).
tff(107,plain,
(paul = |'mary'|),
inference(unit_resolution,[status(thm)],[106, 84])).
tff(108,plain,
(|'mary'| = paul),
inference(symmetry,[status(thm)],[107])).
tff(109,plain,
((mary = |'mary'|) <=> (mary = paul)),
inference(monotonicity,[status(thm)],[108])).
tff(110,plain,
((mary = paul) <=> (mary = |'mary'|)),
inference(symmetry,[status(thm)],[109])).
tff(111,plain,
((~(mary = paul)) <=> (~(mary = |'mary'|))),
inference(monotonicity,[status(thm)],[110])).
tff(112,plain,
((~(mary = paul)) <=> (~(mary = paul))),
inference(rewrite,[status(thm)],[])).
tff(113,plain,
(((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))) & (~(paul = mary))),
inference(and_elim,[status(thm)],[59])).
tff(114,plain,
((((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))) & (~(mary = lucy))),
inference(and_elim,[status(thm)],[113])).
tff(115,plain,
(((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))) & (~(mary = susan))),
inference(and_elim,[status(thm)],[114])).
tff(116,plain,
((((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))) & (~(mary = john))),
inference(and_elim,[status(thm)],[115])).
tff(117,plain,
(((~(mary = paul)) & (~(mary = fred))) & (~(mary = alice))),
inference(and_elim,[status(thm)],[116])).
tff(118,plain,
((~(mary = paul)) & (~(mary = fred))),
inference(and_elim,[status(thm)],[117])).
tff(119,plain,
(~(mary = paul)),
inference(and_elim,[status(thm)],[118])).
tff(120,plain,
(~(mary = paul)),
inference(modus_ponens,[status(thm)],[119, 112])).
tff(121,plain,
(~(mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[120, 111])).
tff(122,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(123,plain,
(room(mary)),
inference(and_elim,[status(thm)],[97])).
tff(124,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[123, 122])).
tff(125,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(126,plain,
(((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary))) <=> ((~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(127,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|)))),
inference(monotonicity,[status(thm)],[126])).
tff(128,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|))),
inference(transitivity,[status(thm)],[127, 125])).
tff(129,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((mary = |'paul'|) | (mary = |'mary'|) | (~room(mary)))),
inference(quant_inst,[status(thm)],[])).
tff(130,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(mary)) | (mary = |'paul'|) | (mary = |'mary'|)),
inference(modus_ponens,[status(thm)],[129, 128])).
tff(131,plain,
((mary = |'paul'|) | (mary = |'mary'|)),
inference(unit_resolution,[status(thm)],[130, 124, 95])).
tff(132,plain,
(mary = |'paul'|),
inference(unit_resolution,[status(thm)],[131, 121])).
tff(133,plain,
(mary = X!0),
inference(transitivity,[status(thm)],[132, 3])).
tff(134,plain,
(older(fred, mary) <=> older(fred, X!0)),
inference(monotonicity,[status(thm)],[133])).
tff(135,plain,
(older(fred, X!0) <=> older(fred, mary)),
inference(symmetry,[status(thm)],[134])).
tff(136,plain,
(older(fred, mary)),
inference(modus_ponens,[status(thm)],[15, 135])).
tff(137,plain,
($false),
inference(unit_resolution,[status(thm)],[1, 136])).
tff(138,plain,((~(X!0 = |'paul'|)) | older(fred, mary)), inference(lemma,lemma(discharge,[]))).
tff(139,plain,
(~(X!0 = |'paul'|)),
inference(unit_resolution,[status(thm)],[138, 1])).
tff(140,plain,
(room(X!0)),
inference(or_elim,[status(thm)],[13])).
tff(141,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(X!0)) | (X!0 = |'paul'|) | (X!0 = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(X!0)) | (X!0 = |'paul'|) | (X!0 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(142,plain,
(((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0))) <=> ((~room(X!0)) | (X!0 = |'paul'|) | (X!0 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(143,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(X!0)) | (X!0 = |'paul'|) | (X!0 = |'mary'|)))),
inference(monotonicity,[status(thm)],[142])).
tff(144,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(X!0)) | (X!0 = |'paul'|) | (X!0 = |'mary'|))),
inference(transitivity,[status(thm)],[143, 141])).
tff(145,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!0 = |'paul'|) | (X!0 = |'mary'|) | (~room(X!0)))),
inference(quant_inst,[status(thm)],[])).
tff(146,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(X!0)) | (X!0 = |'paul'|) | (X!0 = |'mary'|)),
inference(modus_ponens,[status(thm)],[145, 144])).
tff(147,plain,
((X!0 = |'paul'|) | (X!0 = |'mary'|)),
inference(unit_resolution,[status(thm)],[146, 95, 140])).
tff(148,plain,
(X!0 = |'mary'|),
inference(unit_resolution,[status(thm)],[147, 139])).
tff(149,plain,
(|'mary'| = X!0),
inference(symmetry,[status(thm)],[148])).
tff(150,assumption,(X!0 = |'mary'|), introduced(assumption)).
tff(151,plain,
(|'mary'| = X!0),
inference(symmetry,[status(thm)],[150])).
tff(152,plain,
(older(fred, |'mary'|) <=> older(fred, X!0)),
inference(monotonicity,[status(thm)],[151])).
tff(153,plain,
(older(fred, X!0) <=> older(fred, |'mary'|)),
inference(symmetry,[status(thm)],[152])).
tff(154,plain,
(older(fred, |'mary'|)),
inference(modus_ponens,[status(thm)],[15, 153])).
tff(155,assumption,(paul = |'mary'|), introduced(assumption)).
tff(156,plain,
(|'mary'| = paul),
inference(symmetry,[status(thm)],[155])).
tff(157,plain,
((fred = |'mary'|) <=> (fred = paul)),
inference(monotonicity,[status(thm)],[156])).
tff(158,plain,
((fred = |'mary'|) <=> (paul = fred)),
inference(transitivity,[status(thm)],[157, 17])).
tff(159,plain,
((paul = fred) <=> (fred = |'mary'|)),
inference(symmetry,[status(thm)],[158])).
tff(160,plain,
((~(paul = fred)) <=> (~(fred = |'mary'|))),
inference(monotonicity,[status(thm)],[159])).
tff(161,plain,
(~(fred = |'mary'|)),
inference(modus_ponens,[status(thm)],[61, 160])).
tff(162,plain,
(older(|'mary'|, fred) <=> older(paul, fred)),
inference(monotonicity,[status(thm)],[156])).
tff(163,plain,
(older(paul, fred) <=> older(|'mary'|, fred)),
inference(symmetry,[status(thm)],[162])).
tff(164,plain,
(older(|'mary'|, fred)),
inference(modus_ponens,[status(thm)],[67, 163])).
tff(165,plain,
(((~![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))) | ((fred = |'mary'|) | (~older(|'mary'|, fred)) | (~older(fred, |'mary'|)))) <=> ((~![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))) | (fred = |'mary'|) | (~older(|'mary'|, fred)) | (~older(fred, |'mary'|)))),
inference(rewrite,[status(thm)],[])).
tff(166,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))) | ((fred = |'mary'|) | (~older(|'mary'|, fred)) | (~older(fred, |'mary'|)))),
inference(quant_inst,[status(thm)],[])).
tff(167,plain,
((~![X: $i, Y: $i] : ((X = Y) | (~older(Y, X)) | (~older(X, Y)))) | (fred = |'mary'|) | (~older(|'mary'|, fred)) | (~older(fred, |'mary'|))),
inference(modus_ponens,[status(thm)],[166, 165])).
tff(168,plain,
((fred = |'mary'|) | (~older(|'mary'|, fred)) | (~older(fred, |'mary'|))),
inference(unit_resolution,[status(thm)],[167, 77])).
tff(169,plain,
($false),
inference(unit_resolution,[status(thm)],[168, 164, 161, 154])).
tff(170,plain,((~(paul = |'mary'|)) | (~(X!0 = |'mary'|))), inference(lemma,lemma(discharge,[]))).
tff(171,plain,
(~(paul = |'mary'|)),
inference(unit_resolution,[status(thm)],[170, 148])).
tff(172,plain,
(paul = |'paul'|),
inference(unit_resolution,[status(thm)],[106, 171])).
tff(173,plain,
(|'paul'| = paul),
inference(symmetry,[status(thm)],[172])).
tff(174,plain,
((mary = |'paul'|) <=> (mary = paul)),
inference(monotonicity,[status(thm)],[173])).
tff(175,plain,
((mary = paul) <=> (mary = |'paul'|)),
inference(symmetry,[status(thm)],[174])).
tff(176,plain,
((~(mary = paul)) <=> (~(mary = |'paul'|))),
inference(monotonicity,[status(thm)],[175])).
tff(177,plain,
(~(mary = |'paul'|)),
inference(modus_ponens,[status(thm)],[120, 176])).
tff(178,plain,
(mary = |'mary'|),
inference(unit_resolution,[status(thm)],[131, 177])).
tff(179,plain,
(mary = X!0),
inference(transitivity,[status(thm)],[178, 149])).
tff(180,plain,
(older(fred, mary) <=> older(fred, X!0)),
inference(monotonicity,[status(thm)],[179])).
tff(181,plain,
(older(fred, X!0) <=> older(fred, mary)),
inference(symmetry,[status(thm)],[180])).
tff(182,plain,
(older(fred, mary)),
inference(modus_ponens,[status(thm)],[15, 181])).
tff(183,plain,
($false),
inference(unit_resolution,[status(thm)],[1, 182])).
tff(184,plain,(older(fred, mary)), inference(lemma,lemma(discharge,[]))).
tff(185,plain,
(((~room(mary)) | (~room(paul)) | (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~older(fred, mary))) <=> ((~room(mary)) | (~room(paul)) | (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~older(fred, mary)))),
inference(rewrite,[status(thm)],[])).
tff(186,plain,
((~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) <=> (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1))))),
inference(rewrite,[status(thm)],[])).
tff(187,plain,
(((~room(mary)) | (~room(paul)) | (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~older(fred, mary))) <=> ((~room(mary)) | (~room(paul)) | (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~older(fred, mary)))),
inference(monotonicity,[status(thm)],[186])).
tff(188,plain,
(((~room(mary)) | (~room(paul)) | (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~older(fred, mary))) <=> ((~room(mary)) | (~room(paul)) | (~((X!1 = |'paul'|) | (X!1 = |'mary'|) | (~room(X!1)))) | (~older(fred, mary)))),
inference(transitivity,[status(thm)],[187, 185])).
tff(189,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & older(fred, mary)) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & older(fred, mary))),
inference(rewrite,[status(thm)],[])).
tff(190,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & older(fred, mary))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & older(fred, mary)))),
inference(monotonicity,[status(thm)],[189])).
tff(191,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & older(fred, mary))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & older(fred, mary)))),
inference(rewrite,[status(thm)],[])).
tff(192,plain,
((~(((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & older(fred, mary))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & older(fred, mary)))),
inference(rewrite,[status(thm)],[])).
tff(193,axiom,(~(((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & older(fred, mary))), file('/mnt/tmpfs//393391041369572684458198.p','hypothesis')).
tff(194,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & older(fred, mary))),
inference(modus_ponens,[status(thm)],[193, 192])).
tff(195,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & older(fred, mary))),
inference(modus_ponens,[status(thm)],[194, 190])).
tff(196,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & older(fred, mary))),
inference(modus_ponens,[status(thm)],[195, 191])).
tff(197,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & older(fred, mary))),
inference(modus_ponens,[status(thm)],[196, 190])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!1 |'paul'|) (= X!1 |'mary'|) (not (room X!1)))))
(a!5 (refl (~ (not (older fred mary)) (not (older fred mary))))))
(let ((a!6 (~ (not (and (room mary) (room paul) a!3 (older fred mary)))
(or (not (room mary))
(not (room paul))
a!4
(not (older fred mary))))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) a!5 a!6)))
|
Erin, Linda are the only persons in the room.
Only one person in the room who is quiet either is quiet or is rich but not both.
Erin is a sibling of Angelo.
More than one person in the room is creative. | Everyone in the room is creative. | entailment | room(erin)&room(linda)&(![X]:(room(X)=>(X='erin'|X='linda')))&
((((?[X]:(room(X)&((quiet(X))=>(((quiet(X))<~>(rich(X)))))))&(![X,Y]:((room(X)&room(Y)&(((quiet(X))=>(((quiet(X))<~>(rich(X))))))&(((quiet(Y))=>(((quiet(Y))<~>(rich(Y)))))))=>(X=Y)))))&
(sibling(angelo,erin))&
((?[X,Y]:(room(X)&room(Y)&(creative(X)&creative(Y))&(X!=Y))))) | room(erin)&room(linda)&(![X]:(room(X)=>(X='erin'|X='linda')))&
(![X]:(room(X)=>(creative(X)))) | contradiction | [
"p3",
"p0",
"hypothesis"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(room_type, type, (
room: $i > $o)).
tff(tptp_fun_X_3_type, type, (
tptp_fun_X_3: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun_X_4_type, type, (
tptp_fun_X_4: $i)).
tff(creative_type, type, (
creative: $i > $o)).
tff(tptp_fun_Y_1_type, type, (
tptp_fun_Y_1: $i)).
tff(tptp_fun_X_2_type, type, (
tptp_fun_X_2: $i)).
tff(paul_type, type, (
paul: $i)).
tff(mary_type, type, (
mary: $i)).
tff(1,assumption,(~(creative(X!4) | (~room(X!4)))), introduced(assumption)).
tff(2,plain,
((creative(X!4) | (~room(X!4))) | room(X!4)),
inference(tautology,[status(thm)],[])).
tff(3,plain,
(room(X!4)),
inference(unit_resolution,[status(thm)],[2, 1])).
tff(4,plain,
((creative(X!4) | (~room(X!4))) | (~creative(X!4))),
inference(tautology,[status(thm)],[])).
tff(5,plain,
(~creative(X!4)),
inference(unit_resolution,[status(thm)],[4, 1])).
tff(6,assumption,(~creative(X!4)), introduced(assumption)).
tff(7,assumption,(room(X!4)), introduced(assumption)).
tff(8,assumption,(~(X!4 = Y!1)), introduced(assumption)).
tff(9,assumption,(Y!1 = |'mary'|), introduced(assumption)).
tff(10,plain,
(|'mary'| = Y!1),
inference(symmetry,[status(thm)],[9])).
tff(11,plain,
((X!2 = |'mary'|) <=> (X!2 = Y!1)),
inference(monotonicity,[status(thm)],[10])).
tff(12,plain,
((X!2 = Y!1) <=> (X!2 = |'mary'|)),
inference(symmetry,[status(thm)],[11])).
tff(13,plain,
((~(X!2 = Y!1)) <=> (~(X!2 = |'mary'|))),
inference(monotonicity,[status(thm)],[12])).
tff(14,plain,
(?[X: $i, Y: $i] : (room(X) & room(Y) & creative(X) & creative(Y) & (~(X = Y))) <=> ?[X: $i, Y: $i] : (room(X) & room(Y) & creative(X) & creative(Y) & (~(X = Y)))),
inference(rewrite,[status(thm)],[])).
tff(15,plain,
(^[X: $i, Y: $i] : trans(monotonicity(rewrite(((room(X) & room(Y)) & (creative(X) & creative(Y))) <=> (room(X) & room(Y) & creative(X) & creative(Y))), ((((room(X) & room(Y)) & (creative(X) & creative(Y))) & (~(X = Y))) <=> ((room(X) & room(Y) & creative(X) & creative(Y)) & (~(X = Y))))), rewrite(((room(X) & room(Y) & creative(X) & creative(Y)) & (~(X = Y))) <=> (room(X) & room(Y) & creative(X) & creative(Y) & (~(X = Y)))), ((((room(X) & room(Y)) & (creative(X) & creative(Y))) & (~(X = Y))) <=> (room(X) & room(Y) & creative(X) & creative(Y) & (~(X = Y)))))),
inference(bind,[status(th)],[])).
tff(16,plain,
(?[X: $i, Y: $i] : (((room(X) & room(Y)) & (creative(X) & creative(Y))) & (~(X = Y))) <=> ?[X: $i, Y: $i] : (room(X) & room(Y) & creative(X) & creative(Y) & (~(X = Y)))),
inference(quant_intro,[status(thm)],[15])).
tff(17,axiom,(?[X: $i, Y: $i] : (((room(X) & room(Y)) & (creative(X) & creative(Y))) & (~(X = Y)))), file('/mnt/tmpfs//8831644376216498913338284.p','p3')).
tff(18,plain,
(?[X: $i, Y: $i] : (room(X) & room(Y) & creative(X) & creative(Y) & (~(X = Y)))),
inference(modus_ponens,[status(thm)],[17, 16])).
tff(19,plain,
(?[X: $i, Y: $i] : (room(X) & room(Y) & creative(X) & creative(Y) & (~(X = Y)))),
inference(modus_ponens,[status(thm)],[18, 14])).
tff(20,plain,(
room(X!2) & room(Y!1) & creative(X!2) & creative(Y!1) & (~(X!2 = Y!1))),
inference(skolemize,[status(sab)],[19])).
tff(21,plain,
(~(X!2 = Y!1)),
inference(and_elim,[status(thm)],[20])).
tff(22,plain,
(~(X!2 = |'mary'|)),
inference(modus_ponens,[status(thm)],[21, 13])).
tff(23,plain,
(room(X!2)),
inference(and_elim,[status(thm)],[20])).
tff(24,plain,
(^[X: $i] : refl(((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(25,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[24])).
tff(26,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(rewrite,[status(thm)],[])).
tff(27,plain,
(^[X: $i] : rewrite((room(X) => ((X = |'mary'|) | (X = |'paul'|))) <=> ((X = |'paul'|) | (X = |'mary'|) | (~room(X))))),
inference(bind,[status(th)],[])).
tff(28,plain,
(![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|))) <=> ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(quant_intro,[status(thm)],[27])).
tff(29,axiom,((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))), file('/mnt/tmpfs//8831644376216498913338284.p','p0')).
tff(30,plain,
(![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))),
inference(and_elim,[status(thm)],[29])).
tff(31,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[30, 28])).
tff(32,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[31, 26])).
tff(33,plain,(
![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(skolemize,[status(sab)],[32])).
tff(34,plain,
(![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))),
inference(modus_ponens,[status(thm)],[33, 25])).
tff(35,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(X!2)) | (X!2 = |'paul'|) | (X!2 = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(X!2)) | (X!2 = |'paul'|) | (X!2 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(36,plain,
(((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2))) <=> ((~room(X!2)) | (X!2 = |'paul'|) | (X!2 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(37,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(X!2)) | (X!2 = |'paul'|) | (X!2 = |'mary'|)))),
inference(monotonicity,[status(thm)],[36])).
tff(38,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(X!2)) | (X!2 = |'paul'|) | (X!2 = |'mary'|))),
inference(transitivity,[status(thm)],[37, 35])).
tff(39,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!2 = |'paul'|) | (X!2 = |'mary'|) | (~room(X!2)))),
inference(quant_inst,[status(thm)],[])).
tff(40,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(X!2)) | (X!2 = |'paul'|) | (X!2 = |'mary'|)),
inference(modus_ponens,[status(thm)],[39, 38])).
tff(41,plain,
((X!2 = |'paul'|) | (X!2 = |'mary'|)),
inference(unit_resolution,[status(thm)],[40, 34, 23])).
tff(42,plain,
(X!2 = |'paul'|),
inference(unit_resolution,[status(thm)],[41, 22])).
tff(43,plain,
(|'paul'| = X!2),
inference(symmetry,[status(thm)],[42])).
tff(44,plain,
((X!4 = |'mary'|) <=> (X!4 = Y!1)),
inference(monotonicity,[status(thm)],[10])).
tff(45,plain,
((X!4 = Y!1) <=> (X!4 = |'mary'|)),
inference(symmetry,[status(thm)],[44])).
tff(46,plain,
((~(X!4 = Y!1)) <=> (~(X!4 = |'mary'|))),
inference(monotonicity,[status(thm)],[45])).
tff(47,plain,
(~(X!4 = |'mary'|)),
inference(modus_ponens,[status(thm)],[8, 46])).
tff(48,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(X!4)) | (X!4 = |'paul'|) | (X!4 = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(X!4)) | (X!4 = |'paul'|) | (X!4 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(49,plain,
(((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4))) <=> ((~room(X!4)) | (X!4 = |'paul'|) | (X!4 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(50,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(X!4)) | (X!4 = |'paul'|) | (X!4 = |'mary'|)))),
inference(monotonicity,[status(thm)],[49])).
tff(51,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(X!4)) | (X!4 = |'paul'|) | (X!4 = |'mary'|))),
inference(transitivity,[status(thm)],[50, 48])).
tff(52,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((X!4 = |'paul'|) | (X!4 = |'mary'|) | (~room(X!4)))),
inference(quant_inst,[status(thm)],[])).
tff(53,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(X!4)) | (X!4 = |'paul'|) | (X!4 = |'mary'|)),
inference(modus_ponens,[status(thm)],[52, 51])).
tff(54,plain,
((X!4 = |'paul'|) | (X!4 = |'mary'|)),
inference(unit_resolution,[status(thm)],[53, 34, 7])).
tff(55,plain,
(X!4 = |'paul'|),
inference(unit_resolution,[status(thm)],[54, 47])).
tff(56,plain,
(X!4 = X!2),
inference(transitivity,[status(thm)],[55, 43])).
tff(57,plain,
(creative(X!4) <=> creative(X!2)),
inference(monotonicity,[status(thm)],[56])).
tff(58,plain,
(creative(X!2) <=> creative(X!4)),
inference(symmetry,[status(thm)],[57])).
tff(59,plain,
(creative(X!2)),
inference(and_elim,[status(thm)],[20])).
tff(60,plain,
(creative(X!4)),
inference(modus_ponens,[status(thm)],[59, 58])).
tff(61,plain,
($false),
inference(unit_resolution,[status(thm)],[6, 60])).
tff(62,plain,((~(Y!1 = |'mary'|)) | creative(X!4) | (~room(X!4)) | (X!4 = Y!1)), inference(lemma,lemma(discharge,[]))).
tff(63,plain,
(~(Y!1 = |'mary'|)),
inference(unit_resolution,[status(thm)],[62, 8, 7, 6])).
tff(64,plain,
(room(Y!1)),
inference(and_elim,[status(thm)],[20])).
tff(65,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(Y!1)) | (Y!1 = |'paul'|) | (Y!1 = |'mary'|))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(Y!1)) | (Y!1 = |'paul'|) | (Y!1 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(66,plain,
(((Y!1 = |'paul'|) | (Y!1 = |'mary'|) | (~room(Y!1))) <=> ((~room(Y!1)) | (Y!1 = |'paul'|) | (Y!1 = |'mary'|))),
inference(rewrite,[status(thm)],[])).
tff(67,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((Y!1 = |'paul'|) | (Y!1 = |'mary'|) | (~room(Y!1)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((~room(Y!1)) | (Y!1 = |'paul'|) | (Y!1 = |'mary'|)))),
inference(monotonicity,[status(thm)],[66])).
tff(68,plain,
(((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((Y!1 = |'paul'|) | (Y!1 = |'mary'|) | (~room(Y!1)))) <=> ((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(Y!1)) | (Y!1 = |'paul'|) | (Y!1 = |'mary'|))),
inference(transitivity,[status(thm)],[67, 65])).
tff(69,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | ((Y!1 = |'paul'|) | (Y!1 = |'mary'|) | (~room(Y!1)))),
inference(quant_inst,[status(thm)],[])).
tff(70,plain,
((~![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X)))) | (~room(Y!1)) | (Y!1 = |'paul'|) | (Y!1 = |'mary'|)),
inference(modus_ponens,[status(thm)],[69, 68])).
tff(71,plain,
((Y!1 = |'paul'|) | (Y!1 = |'mary'|)),
inference(unit_resolution,[status(thm)],[70, 34, 64])).
tff(72,plain,
(Y!1 = |'paul'|),
inference(unit_resolution,[status(thm)],[71, 63])).
tff(73,plain,
(|'paul'| = Y!1),
inference(symmetry,[status(thm)],[72])).
tff(74,plain,
((X!2 = |'paul'|) <=> (X!2 = Y!1)),
inference(monotonicity,[status(thm)],[73])).
tff(75,plain,
((X!2 = Y!1) <=> (X!2 = |'paul'|)),
inference(symmetry,[status(thm)],[74])).
tff(76,plain,
((~(X!2 = Y!1)) <=> (~(X!2 = |'paul'|))),
inference(monotonicity,[status(thm)],[75])).
tff(77,plain,
(~(X!2 = |'paul'|)),
inference(modus_ponens,[status(thm)],[21, 76])).
tff(78,plain,
(X!2 = |'mary'|),
inference(unit_resolution,[status(thm)],[41, 77])).
tff(79,plain,
(|'mary'| = X!2),
inference(symmetry,[status(thm)],[78])).
tff(80,plain,
((X!4 = |'paul'|) <=> (X!4 = Y!1)),
inference(monotonicity,[status(thm)],[73])).
tff(81,plain,
((X!4 = Y!1) <=> (X!4 = |'paul'|)),
inference(symmetry,[status(thm)],[80])).
tff(82,plain,
((~(X!4 = Y!1)) <=> (~(X!4 = |'paul'|))),
inference(monotonicity,[status(thm)],[81])).
tff(83,plain,
(~(X!4 = |'paul'|)),
inference(modus_ponens,[status(thm)],[8, 82])).
tff(84,plain,
(X!4 = |'mary'|),
inference(unit_resolution,[status(thm)],[54, 83])).
tff(85,plain,
(X!4 = X!2),
inference(transitivity,[status(thm)],[84, 79])).
tff(86,plain,
(creative(X!4) <=> creative(X!2)),
inference(monotonicity,[status(thm)],[85])).
tff(87,plain,
(creative(X!2) <=> creative(X!4)),
inference(symmetry,[status(thm)],[86])).
tff(88,plain,
(creative(X!4)),
inference(modus_ponens,[status(thm)],[59, 87])).
tff(89,plain,
($false),
inference(unit_resolution,[status(thm)],[6, 88])).
tff(90,plain,((X!4 = Y!1) | creative(X!4) | (~room(X!4))), inference(lemma,lemma(discharge,[]))).
tff(91,plain,
(X!4 = Y!1),
inference(unit_resolution,[status(thm)],[90, 5, 3])).
tff(92,plain,
(creative(X!4) <=> creative(Y!1)),
inference(monotonicity,[status(thm)],[91])).
tff(93,plain,
(creative(Y!1) <=> creative(X!4)),
inference(symmetry,[status(thm)],[92])).
tff(94,plain,
(creative(Y!1)),
inference(and_elim,[status(thm)],[20])).
tff(95,plain,
(creative(X!4)),
inference(modus_ponens,[status(thm)],[94, 93])).
tff(96,plain,
($false),
inference(unit_resolution,[status(thm)],[5, 95])).
tff(97,plain,(creative(X!4) | (~room(X!4))), inference(lemma,lemma(discharge,[]))).
tff(98,plain,
(room(paul) <=> room(paul)),
inference(rewrite,[status(thm)],[])).
tff(99,plain,
(room(mary) & room(paul)),
inference(and_elim,[status(thm)],[29])).
tff(100,plain,
(room(paul)),
inference(and_elim,[status(thm)],[99])).
tff(101,plain,
(room(paul)),
inference(modus_ponens,[status(thm)],[100, 98])).
tff(102,plain,
(room(mary) <=> room(mary)),
inference(rewrite,[status(thm)],[])).
tff(103,plain,
(room(mary)),
inference(and_elim,[status(thm)],[99])).
tff(104,plain,
(room(mary)),
inference(modus_ponens,[status(thm)],[103, 102])).
tff(105,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(creative(X!4) | (~room(X!4))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(creative(X!4) | (~room(X!4)))))),
inference(rewrite,[status(thm)],[])).
tff(106,plain,
((~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) <=> (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3))))),
inference(rewrite,[status(thm)],[])).
tff(107,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(creative(X!4) | (~room(X!4))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(creative(X!4) | (~room(X!4)))))),
inference(monotonicity,[status(thm)],[106])).
tff(108,plain,
(((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(creative(X!4) | (~room(X!4))))) <=> ((~room(mary)) | (~room(paul)) | (~((X!3 = |'paul'|) | (X!3 = |'mary'|) | (~room(X!3)))) | (~(creative(X!4) | (~room(X!4)))))),
inference(transitivity,[status(thm)],[107, 105])).
tff(109,plain,
((room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (creative(X) | (~room(X)))) <=> (room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (creative(X) | (~room(X))))),
inference(rewrite,[status(thm)],[])).
tff(110,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (creative(X) | (~room(X))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (creative(X) | (~room(X)))))),
inference(monotonicity,[status(thm)],[109])).
tff(111,plain,
((~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (creative(X) | (~room(X))))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (creative(X) | (~room(X)))))),
inference(rewrite,[status(thm)],[])).
tff(112,plain,
((~(((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ![X: $i] : (room(X) => creative(X)))) <=> (~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (creative(X) | (~room(X)))))),
inference(rewrite,[status(thm)],[])).
tff(113,axiom,(~(((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & ![X: $i] : (room(X) => creative(X)))), file('/mnt/tmpfs//8831644376216498913338284.p','hypothesis')).
tff(114,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (creative(X) | (~room(X))))),
inference(modus_ponens,[status(thm)],[113, 112])).
tff(115,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (creative(X) | (~room(X))))),
inference(modus_ponens,[status(thm)],[114, 110])).
tff(116,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (creative(X) | (~room(X))))),
inference(modus_ponens,[status(thm)],[115, 111])).
tff(117,plain,
(~(room(mary) & room(paul) & ![X: $i] : ((X = |'paul'|) | (X = |'mary'|) | (~room(X))) & ![X: $i] : (creative(X) | (~room(X))))),
inference(modus_ponens,[status(thm)],[116, 110])).
unexpected number of arguments: (let ((a!1 (refl (~ (not (room mary)) (not (room mary)))))
(a!2 (refl (~ (not (room paul)) (not (room paul)))))
(a!3 (forall ((X $i)) (or (= X |'paul'|) (= X |'mary'|) (not (room X)))))
(a!4 (not (or (= X!3 |'paul'|) (= X!3 |'mary'|) (not (room X!3)))))
(a!5 (forall ((X $i)) (or (creative X) (not (room X)))))
(a!6 (not (or (creative X!4) (not (room X!4))))))
(let ((a!7 (~ (not (and (room mary) (room paul) a!3 a!5))
(or (not (room mary)) (not (room paul)) a!4 a!6))))
(nnf-neg a!1 a!2 (sk (~ (not a!3) a!4)) (sk (~ (not a!5) a!6)) a!7)))
|
Anneliese, Damian are the only persons in the room. Someone in the room is quiet. Not everyone outside the room either is quieter than Marietta or is not a quiet person but not both. Not everyone in the room is richer than Marietta, is wise and is not a wise happy person. Anneliese is not a quiet person or is not quiet, not happy, not rich or both if he/she either is not happy or is happy but not both. Everyone in the room is not a wise person only if they is a quiet happy person, is quiet and is not wise, not rich. Not everyone in the room is rich. Only one person in the room is rich. Someone in the room is a wise person if they is wise. Damian is richer than Marietta or is not quiet, not happy or both if he/she is a happy person, is not a quiet wise happy person and is rich. Damian is a quiet happy person if he/she is happy and is quieter than Marietta. | Damian is happy. | neutral | room(anneliese)&room(damian)&(![X]:(room(X)=>(X='anneliese'|X='damian')))&
((?[X]:(room(X)=>(quiet(X))))&
(~![X]:(~room(X)=>(((quieter(marietta,X))<~>(~(quiet(X)&person(X)))))))&
(~![X]:(room(X)=>(((richer(marietta,X))&(wise(X))&(~(wise(X)&happy(X)&person(X)))))))&
(((((~happy(anneliese))<~>(happy(anneliese))))=>(((~(quiet(anneliese)&person(anneliese)))|(~quiet(anneliese)&~happy(anneliese)&~rich(anneliese))))))&
(![X]:(room(X)=>(((((quiet(X)&happy(X)&person(X))&(quiet(X))&(~wise(X)&~rich(X))))<=(~(wise(X)&person(X)))))))&
(~![X]:(room(X)=>(rich(X))))&
(((?[X]:(room(X)&rich(X)))&(![X,Y]:((room(X)&room(Y)&(rich(X))&(rich(Y)))=>(X=Y)))))&
(?[X]:(room(X)=>(((wise(X))=>(wise(X)&person(X))))))&
(((((happy(damian)&person(damian))&(~(quiet(damian)&wise(damian)&happy(damian)&person(damian)))&(rich(damian))))=>(((richer(marietta,damian))|(~quiet(damian)&~happy(damian))))))&
(((((happy(damian))&(quieter(marietta,damian))))=>(quiet(damian)&happy(damian)&person(damian))))) | room(anneliese)&room(damian)&(![X]:(room(X)=>(X='anneliese'|X='damian')))&
(happy(damian)) | contradiction | [] | null |
Charles, Doris are the only persons in the room.
Lois and Anthony hate each other.
At least one person in the room predf.
Not everyone in the room is hated by Anthony.
Doris predf, is hated by Anthony and is hated by Lois. | Charles predf. | neutral | room(charles)&room(doris)&(![X]:(room(X)=>(X='charles'|X='doris')))&
(((hate(lois,anthony) & hate(anthony,lois)))&
(((?[X]:(room(X)&predf(X)))))&
(~![X]:(room(X)=>(hate(X,anthony))))&
(((predf(doris))&(hate(doris,anthony))&(hate(doris,lois))))) | room(charles)&room(doris)&(![X]:(room(X)=>(X='charles'|X='doris')))&
(predf(charles)) | entailment | [] | null |
Charles, Leroy are the only persons in the room. Either “Charles is older than William” or “only one person in the room who likes William enjoys fishing” or but not both. “Leroy who is not brave is richer than William” unless “everyone outside the room is brave only if they is liked by William”. If “someone in the room is not liked by William” then “Charles and William like each other”. Someone who likes William if they does not enjoy fishing and is rich like someone who is a client of William. Leroy enjoys fishing. At least one person in the room is a client of William. Leroy who likes William is liked by William. Charles is not old if he/she does not enjoy fishing. | William is older than Charles. | neutral | room(charles)&room(leroy)&(![X]:(room(X)=>(X='charles'|X='leroy')))&
(((older(william,charles))<~>(((?[X]:(room(X)&((like(william,X))=>(enjoys_fishing(X)))))&(![X,Y]:((room(X)&room(Y)&(((like(william,X))=>(enjoys_fishing(X))))&(((like(william,Y))=>(enjoys_fishing(Y)))))=>(X=Y))))))&
(~(![X]:(~room(X)=>(((like(X,william))<=(brave(X))))))=>((~brave(leroy))&(richer(william,leroy))))&
((?[X]:(room(X)=>(~like(X,william))))=>((like(charles,william) & like(william,charles))))&
(?[X,Y]:((((((does_not_enjoy_fishing(X))&(rich(X))))=>(like(william,X))))&(client(william,Y))&(like(X,Y))))&
(enjoys_fishing(leroy))&
(((?[X]:(room(X)&client(william,X)))))&
((like(william,leroy))&(like(leroy,william)))&
(((does_not_enjoy_fishing(charles))=>(~old(charles))))) | room(charles)&room(leroy)&(![X]:(room(X)=>(X='charles'|X='leroy')))&
(older(charles,william)) | contradiction | [] | null |
Amanda, Mary are the only persons in the room.
“Amanda ~predf” unless “Amanda predf if he/she ~predf”.
Amanda either predf or does not practice kickboxing but not both.
Amanda either is brave or practices kickboxing but not both if he/she is a brave person.
Only one person in the room either is brave or predf but not both. | Amanda either predf or practices kickboxing but not both. | contradiction | room(amanda)&room(mary)&(![X]:(room(X)=>(X='amanda'|X='mary')))&
((~(((~predf(amanda))=>(predf(amanda))))=>(~predf(amanda)))&
(((predf(amanda))<~>(does_not_practice_kickboxing(amanda))))&
(((brave(amanda)&person(amanda))=>(((brave(amanda))<~>(practices_kickboxing(amanda))))))&
(((?[X]:(room(X)&((brave(X))<~>(predf(X)))))&(![X,Y]:((room(X)&room(Y)&(((brave(X))<~>(predf(X))))&(((brave(Y))<~>(predf(Y)))))=>(X=Y)))))) | room(amanda)&room(mary)&(![X]:(room(X)=>(X='amanda'|X='mary')))&
(((predf(amanda))<~>(practices_kickboxing(amanda)))) | entailment | [
"p2",
"hypothesis"
] | % SZS status Unsatisfiable
% SZS output start Proof
tff(predb_type, type, (
predb: $i > $o)).
tff(mary_type, type, (
mary: $i)).
tff(predf_type, type, (
predf: $i > $o)).
tff(tptp_fun__paul__type, type, (
tptp_fun__paul_: $i)).
tff(tptp_fun__mary__type, type, (
tptp_fun__mary_: $i)).
tff(room_type, type, (
room: $i > $o)).
tff(paul_type, type, (
paul: $i)).
tff(1,assumption,(predb(mary)), introduced(assumption)).
tff(2,plain,
((predb(mary) <=> predf(mary)) <=> (predb(mary) <=> predf(mary))),
inference(rewrite,[status(thm)],[])).
tff(3,plain,
((~(~(predb(mary) <=> predf(mary)))) <=> (predb(mary) <=> predf(mary))),
inference(rewrite,[status(thm)],[])).
tff(4,plain,
((~(predb(mary) <=> predf(mary))) <=> (~(predb(mary) <=> predf(mary)))),
inference(rewrite,[status(thm)],[])).
tff(5,plain,
((predf(mary) <=> (~predb(mary))) <=> (~(predb(mary) <=> predf(mary)))),
inference(rewrite,[status(thm)],[])).
tff(6,plain,
((predf(mary) <=> (~predb(mary))) <=> (~(predb(mary) <=> predf(mary)))),
inference(transitivity,[status(thm)],[5, 4])).
tff(7,plain,
((~(predf(mary) <=> (~predb(mary)))) <=> (~(~(predb(mary) <=> predf(mary))))),
inference(monotonicity,[status(thm)],[6])).
tff(8,plain,
((~(predf(mary) <=> (~predb(mary)))) <=> (predb(mary) <=> predf(mary))),
inference(transitivity,[status(thm)],[7, 3])).
tff(9,axiom,(~(predf(mary) <=> (~predb(mary)))), file('/mnt/tmpfs//257370384768358926520696.p','p2')).
tff(10,plain,
(predb(mary) <=> predf(mary)),
inference(modus_ponens,[status(thm)],[9, 8])).
tff(11,plain,
(predb(mary) <=> predf(mary)),
inference(modus_ponens,[status(thm)],[10, 2])).
tff(12,plain,
((~predb(mary)) | predf(mary) | (~(predb(mary) <=> predf(mary)))),
inference(tautology,[status(thm)],[])).
tff(13,plain,
((~predb(mary)) | predf(mary)),
inference(unit_resolution,[status(thm)],[12, 11])).
tff(14,plain,
(predf(mary)),
inference(unit_resolution,[status(thm)],[13, 1])).
tff(15,plain,
((~(predf(mary) <=> predb(mary))) <=> (~(predf(mary) <=> predb(mary)))),
inference(rewrite,[status(thm)],[])).
tff(16,axiom,(((room(mary) & room(paul)) & ![X: $i] : (room(X) => ((X = |'mary'|) | (X = |'paul'|)))) & (~(predf(mary) <=> predb(mary)))), file('/mnt/tmpfs//257370384768358926520696.p','hypothesis')).
tff(17,plain,
(~(predf(mary) <=> predb(mary))),
inference(and_elim,[status(thm)],[16])).
tff(18,plain,
(~(predf(mary) <=> predb(mary))),
inference(modus_ponens,[status(thm)],[17, 15])).
tff(19,plain,
(~(predf(mary) <=> predb(mary))),
inference(modus_ponens,[status(thm)],[18, 15])).
tff(20,plain,
(~(predf(mary) <=> predb(mary))),
inference(modus_ponens,[status(thm)],[19, 15])).
tff(21,plain,
(~(predf(mary) <=> predb(mary))),
inference(modus_ponens,[status(thm)],[20, 15])).
tff(22,plain,
(~(predf(mary) <=> predb(mary))),
inference(modus_ponens,[status(thm)],[21, 15])).
tff(23,plain,
((predf(mary) <=> predb(mary)) | (~predf(mary)) | (~predb(mary))),
inference(tautology,[status(thm)],[])).
tff(24,plain,
((~predf(mary)) | (~predb(mary))),
inference(unit_resolution,[status(thm)],[23, 22])).
tff(25,plain,
($false),
inference(unit_resolution,[status(thm)],[24, 14, 1])).
tff(26,plain,(~predb(mary)), inference(lemma,lemma(discharge,[]))).
tff(27,plain,
(predb(mary) | (~predf(mary)) | (~(predb(mary) <=> predf(mary)))),
inference(tautology,[status(thm)],[])).
tff(28,plain,
(predb(mary) | (~predf(mary))),
inference(unit_resolution,[status(thm)],[27, 11])).
tff(29,plain,
(~predf(mary)),
inference(unit_resolution,[status(thm)],[28, 26])).
tff(30,plain,
((predf(mary) <=> predb(mary)) | predf(mary) | predb(mary)),
inference(tautology,[status(thm)],[])).
tff(31,plain,
(predf(mary) | predb(mary)),
inference(unit_resolution,[status(thm)],[30, 22])).
tff(32,plain,
($false),
inference(unit_resolution,[status(thm)],[31, 29, 26])).
% SZS output end Proof
|
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